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Marco Fontana - One of the best experts on this subject based on the ideXlab platform.
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uppers to zero in polynomial rings and prufer like Domains
Communications in Algebra, 2009Co-Authors: Gyu Whan Chang, Marco FontanaAbstract:Let D be an Integral Domain and X an indeterminate over D. It is well known that (a) D is quasi-Prufer (i.e., its Integral closure is a Prufer Domain) if and only if each upper to zero Q in D[X] contains a polynomial g ∈ D[X] with content c D (g) = D; (b) an upper to zero Q in D[X] is a maximal t-ideal if and only if Q contains a nonzero polynomial g ∈ D[X] with c D (g) v = D. Using these facts, the notions of UMt-Domain (i.e., an Integral Domain such that each upper to zero is a maximal t-ideal) and quasi-Prufer Domain can be naturally extended to the semistar operation setting and studied in a unified frame. In this article, given a semistar operation ☆ in the sense of Okabe–Matsuda, we introduce the ☆-quasi-Prufer Domains. We give several characterizations of these Domains and we investigate their relations with the UMt-Domains and the Prufer v-multiplication Domains.
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uppers to zero in polynomial rings and pr ufer like Domains
arXiv: Commutative Algebra, 2008Co-Authors: Gyu Whan Chang, Marco FontanaAbstract:Let $D$ be an Integral Domain and $X$ an indeterminate over $D$. It is well known that (a) $D$ is quasi-Pr\"ufer (i.e, its Integral closure is a Pr\"ufer Domain) if and only if each upper to zero $Q$ in $D[X] $ contains a polynomial $g \in D[X]$ with content $\co_D(g) = D$; (b) an upper to zero $Q$ in $D[X]$ is a maximal $t$-ideal if and only if $Q$ contains a nonzero polynomial $g \in D[X]$ with $\co_D(g)^v = D$. Using these facts, the notions of UM$t$-Domain (i.e., an Integral Domain such that each upper to zero is a maximal $t$-ideal) and quasi-Pr\"ufer Domain can be naturally extended to the semistar operation setting and studied in a unified frame. In this paper, given a semistar operation $\star$ in the sense of Okabe-Matsuda, we introduce the $\star$-quasi-Pr\"ufer Domains. We give several characterizations of these Domains and we investigate their relations with the UM$t$-Domains and the Pr\"ufer $v$-multiplication Domains.
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uppers to zero and semistar operations in polynomial rings
Journal of Algebra, 2007Co-Authors: Gyu Whan Chang, Marco FontanaAbstract:Abstract Given a stable semistar operation of finite type ⋆ on an Integral Domain D, we show that it is possible to define in a canonical way a stable semistar operation of finite type [ ⋆ ] on the polynomial ring D [ X ] , such that D is a ⋆-quasi-Prufer Domain if and only if each upper to zero in D [ X ] is a quasi- [ ⋆ ] -maximal ideal. This result completes the investigation initiated by Houston–Malik–Mott [E. Houston, S. Malik, J. Mott, Characterizations of ∗-multiplication Domains, Canad. Math. Bull. 27 (1984) 48–52, Section 2. [17] ] in the star operation setting. Moreover, we show that D is a Prufer ⋆-multiplication (respectively, a ⋆-Noetherian; a ⋆-Dedekind) Domain if and only if D [ X ] is a Prufer [ ⋆ ] -multiplication (respectively, a [ ⋆ ] -Noetherian; a [ ⋆ ] -Dedekind) Domain. As an application of the techniques introduced here, we obtain a new interpretation of the Gabriel–Popescu localizing systems of finite type on an Integral Domain D (Problem 45 of [S.T. Chapman, S. Glaz, One hundred problems in commutative ring theory, in: S.T. Chapman, S. Glaz (Eds.), Non-Noetherian Commutative Ring Theory, Kluwer Academic Publishers, 2000, pp. 459–476. [4] ]), in terms of multiplicatively closed sets of the polynomial ring D [ X ] .
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uppers to zero and semistar operations in polynomial rings
arXiv: Commutative Algebra, 2007Co-Authors: Gyu Whan Chang, Marco FontanaAbstract:Given a stable semistar operation of finite type $\star$ on an Integral Domain $D$, we show that it is possible to define in a canonical way a stable semistar operation of finite type $[\star]$ on the polynomial ring $D[X]$, such that $D$ is a $\star$-quasi-Pr\"ufer Domain if and only if each upper to zero in $D[X]$ is a quasi-$[\star]$-maximal ideal. This result completes the investigation initiated by Houston-Malik-Mott \cite[Section 2]{hmm} in the star operation setting. Moreover, we show that $D$ is a Pr\"ufer $\star$-multiplication (resp., a $\star$-Noetherian; a $\star$-Dedekind) Domain if and only if $D[X]$ is a Pr\"ufer $[\star]$-multiplication (resp., a $[\star]$-Noetherian; a $[\star]$-Dedekind) Domain. As an application of the techniques introduced here, we obtain a new interpretation of the Gabriel-Popescu localizing systems of finite type on an Integral Domain $D$ (Problem 45 of \cite{cg}), in terms of multiplicatively closed sets of the polynomial ring $D[X]$.
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nagata rings kronecker function rings and related semistar operations
arXiv: Commutative Algebra, 2003Co-Authors: Marco Fontana, Alan K LoperAbstract:In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer's book \cite{G}) and, hence, the related classical theory of ideal systems based on the works by W. Krull, E. Noether, H. Pr\"{u}fer and P. Lorenzen from 1930's. In \cite{FL1} and \cite{FL2} the current authors investigated properties of the Kronecker function rings which arise from arbitrary semistar operations on an Integral Domain $D$. In this paper we extend that study and also generalize Kang's notion of a star Nagata ring \cite{Kang:1987} and \cite{Kang:1989} to the semistar setting. Our principal focuses are the similarities between the ideal structure of the Nagata and Kronecker semistar rings and between the natural semistar operations that these two types of function rings give rise to on $D$.
Gyu Whan Chang - One of the best experts on this subject based on the ideXlab platform.
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Recent results on weakly factorial Domains
EDP Sciences, 2018Co-Authors: Gyu Whan ChangAbstract:In this paper, we will survey recent results on weakly factorial Domains base on the results of [11, 13, 14]. LetD be an Integral Domain, X be an indeterminate over D, d ∈ D, R = D[X,d/X] $P_{\textrm{rad}} \propto P_{\textrm{sw}}^{1.2}$ D[X,dX] be a subring of the Laurent polynomial ring D[X,1/X] $P_{\textrm{rad}} \propto P_{\textrm{sw}}^{1.2}$ D[X,1X] , Γ be a nonzero torsionless commutative cancellative monoid with quotient group G, and D[Γ] be the semigroup ring of Γ over D. Among other things, we show that R is a weakly factorial Domain if and only if D is a weakly factorial GCD‐Domain and d = 0, d is a unit of D or d is a prime element of D. We also show that if char(D) = 0 (resp., char(D) = p > 0), then D[Γ] is a weakly factorial Domain if and only if D is a weakly factorial GCD Domain, Γ is a weakly factorial GCD semigroup, and G is of type (0,0,0,…) (resp., (0,0,0,…) except p)
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rings of formal power series in an infinite set of indeterminates
Communications in Algebra, 2014Co-Authors: Gyu Whan ChangAbstract:Let α be an infinite cardinal number, Λ be an index set of cardinality > α, and {X λ}λ∈Λ be a set of indeterminates over an Integral Domain D. It is well known that there are three ways of defining the ring of formal power series in {X λ}λ∈Λ over D, say, D[[{X λ}]] i for i = 1, 2, 3. In this paper, we let D[[{X λ}]]α = ∪ {D[[{X λ}λ∈Γ]]3 | Γ ⊆ Λ and |Γ| ≤ α}, and we then show that D[[{X λ}]]α is an Integral Domain such that D[[{X λ}]]2 ⊊ D[[{X λ}]]α ⊊ D[[{X λ}]]3. We also prove that (1) D is a Krull Domain if and only if D[[{X λ}]]α is a Krull Domain and (2) D[[{X λ}]]α is a unique factorization Domain (UFD) (resp., π-Domain) if and only if D[[X 1,…, X n ]] is a UFD (resp., π-Domain) for every integer n ≥ 1.
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noetherian Domains and the ring d x n ii
Journal of Korean Medical Science, 2011Co-Authors: Gyu Whan ChangAbstract:Let D be an Integral Domain with quotient field K, X be a nonempty set of indeterminates over D, * be a star operation on D, ={f D[X]|c(f)= D}, be the star operation on D defined by = ID[X] K, and [*] be the star operation on D[X] canonically associated to * as in Theorem 2.1. Let (resp., , ) be the global (resp.,*-global, [*]-global) transform of a ring A. We show that D is a -Noetherian Domain if and only if D[X] is a [*]-Noetherian Domain. We prove that [X] = (D[X]) = (D[X]); hence if D is a -Noetherian Domain, then each ring between D[X] and [X] is a Noetherian Domain. Let = {|P -Max(D) and htP 2}. We show that and study some properties of and .
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uppers to zero in polynomial rings and prufer like Domains
Communications in Algebra, 2009Co-Authors: Gyu Whan Chang, Marco FontanaAbstract:Let D be an Integral Domain and X an indeterminate over D. It is well known that (a) D is quasi-Prufer (i.e., its Integral closure is a Prufer Domain) if and only if each upper to zero Q in D[X] contains a polynomial g ∈ D[X] with content c D (g) = D; (b) an upper to zero Q in D[X] is a maximal t-ideal if and only if Q contains a nonzero polynomial g ∈ D[X] with c D (g) v = D. Using these facts, the notions of UMt-Domain (i.e., an Integral Domain such that each upper to zero is a maximal t-ideal) and quasi-Prufer Domain can be naturally extended to the semistar operation setting and studied in a unified frame. In this article, given a semistar operation ☆ in the sense of Okabe–Matsuda, we introduce the ☆-quasi-Prufer Domains. We give several characterizations of these Domains and we investigate their relations with the UMt-Domains and the Prufer v-multiplication Domains.
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uppers to zero in polynomial rings and pr ufer like Domains
arXiv: Commutative Algebra, 2008Co-Authors: Gyu Whan Chang, Marco FontanaAbstract:Let $D$ be an Integral Domain and $X$ an indeterminate over $D$. It is well known that (a) $D$ is quasi-Pr\"ufer (i.e, its Integral closure is a Pr\"ufer Domain) if and only if each upper to zero $Q$ in $D[X] $ contains a polynomial $g \in D[X]$ with content $\co_D(g) = D$; (b) an upper to zero $Q$ in $D[X]$ is a maximal $t$-ideal if and only if $Q$ contains a nonzero polynomial $g \in D[X]$ with $\co_D(g)^v = D$. Using these facts, the notions of UM$t$-Domain (i.e., an Integral Domain such that each upper to zero is a maximal $t$-ideal) and quasi-Pr\"ufer Domain can be naturally extended to the semistar operation setting and studied in a unified frame. In this paper, given a semistar operation $\star$ in the sense of Okabe-Matsuda, we introduce the $\star$-quasi-Pr\"ufer Domains. We give several characterizations of these Domains and we investigate their relations with the UM$t$-Domains and the Pr\"ufer $v$-multiplication Domains.
L M Yang - One of the best experts on this subject based on the ideXlab platform.
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an immersed boundary simplified sphere function based gas kinetic scheme for simulation of 3d incompressible flows
Physics of Fluids, 2017Co-Authors: L M Yang, Wenming Yang, Yong Wang, J WuAbstract:In this work, an immersed boundary-simplified sphere function-based gas kinetic scheme (SGKS) is presented for the simulation of 3D incompressible flows with curved and moving boundaries. At first, the SGKS [Yang et al., “A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows,” J. Comput. Phys. 295, 322 (2015) and Yang et al., “Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows,” J. Comput. Phys. 319, 129 (2016)], which is often applied for the simulation of compressible flows, is simplified to improve the computational efficiency for the simulation of incompressible flows. In the original SGKS, the Integral Domain along the spherical surface for computing conservative variables and numerical fluxes is usually not symmetric at the cell interface. This leads the expression of numerical fluxes at the cell interface to be relatively complicated. For incompressible flows, the sphere at ...
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circular function based gas kinetic scheme for simulation of inviscid compressible flows
Journal of Computational Physics, 2013Co-Authors: L M Yang, C Shu, Ning ZhaoAbstract:This paper presents a new gas-kinetic scheme for simulation of compressible inviscid flows. It starts to simplify the Integral Domain of Maxwellian distribution function over the phase velocity @x and phase energy @z to the Integral Domain of modified Maxwellian function over the phase velocity @x only. The influence of Integral over phase energy @z is embodied as the particle internal energy e"p. The modified Maxwellian function is further simplified to a circular function with the assumption that all the particles are concentrated on a circle. Then two circular function-based gas-kinetic schemes are presented for simulation of compressible inviscid flows. In the new schemes, no error and exponential functions, which are often appeared in the Maxwellian function-based gas-kinetic schemes, are involved. As a result, the new schemes can be implemented in a more efficient way. To validate the proposed new gas-kinetic schemes, test examples in the transonic flow, supersonic flow and hypersonic flow regimes are solved. Numerical results showed that the solution accuracy of the circular function-based gas-kinetic schemes is comparable to that of corresponding Maxwellian function-based gas-kinetic schemes. However, the circular function-based gas-kinetic schemes need less computational effort.
Licheng Guo - One of the best experts on this subject based on the ideXlab platform.
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A Domain-independent interaction Integral method for evaluating the dynamic stress intensity factors of an interface crack in nonhomogeneous materials
International Journal of Solids and Structures, 2016Co-Authors: Kai Huang, Licheng Guo, Pengfei Jia, Takayuki KitamuraAbstract:Abstract We propose a new Domain-independent interaction Integral (DII-Integral), which can evaluate the dynamic stress intensity factors (DSIFs) of an interface crack in nonhomogeneous materials under dynamic loading conditions. The DII-Integral is rigorously proved to be Domain-independent of arbitrary interfaces emerged in the Integral Domain. Since no material property derivative is involved in the DII-Integral formulation, it can be applied to the interface crack problems with both differentiable and non-differentiable material properties. By using the extended finite element method (XFEM) combined with the DII-Integral, several benchmark problems are investigated to examine the validity of the proposed DII-Integral and the influence of material nonhomogeneity on the DSIFs. The results show that the present DII-Integral is effective and efficient to evaluate the DSIFs of an interface crack in nonhomogeneous materials.
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an interaction energy Integral method for nonhomogeneous materials with interfaces under thermal loading
International Journal of Solids and Structures, 2012Co-Authors: Licheng Guo, Fengnan Guo, Li ZhangAbstract:Abstract A plane crack problem of nonhomogeneous materials with interfaces subjected to static thermal loading is investigated. A modified interaction energy Integral method (IEIM) is developed to obtain the mixed-mode thermal stress intensity factors (TSIFs). Compared with the previous IEIM, the original point of this paper is: the Domain-independence of the modified IEIM still stands in nonhomogeneous materials with interfaces under thermal loading. Therefore, the modified IEIM can still be applied to obtain the TSIFs of nonhomogeneous material even if the Integral Domain includes interfaces. The modified IEIM is combined with the extended finite element method (XFEM) to solve several thermal fracture problems of nonhomogeneous materials. Good agreement can be obtained compared with the analytic solutions and the Domain-independence of the IEIM is verified. Therefore, the present method is effective to study the TSIFs of nonhomogeneous materials even when the materials contain interfaces. The influence of the discontinuity of the material properties (thermal expansion coefficient, thermal conductivity and Young’s modulus) on the TSIFs is investigated. The results show that the discontinuity of both thermal expansion coefficient and Young’s modulus affects the TSIFs greatly, while the discontinuity of thermal conductivity does not arouse obvious change of the TSIFs.
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an interaction Integral method for 3d curved cracks in nonhomogeneous materials with complex interfaces
International Journal of Solids and Structures, 2010Co-Authors: Licheng GuoAbstract:This work derives an interaction Integral for the computation of mixed-mode stress intensity factors (SIFs) in three-dimensional (3D) nonhomogeneous materials with continuous or discontinuous properties. The present method is based on a two-state Integral by the superposition of actual and auxiliary fields. In 3D Domain formulation of the interaction Integral derived here, the integrand does not involve any derivatives of material properties. Furthermore, the formulation can be proved to be still valid even when the Integral Domain contains material interfaces. Therefore, it is not necessary to limit the material properties to be continuous for the present formulation. On account of these advantages, the application range of the interaction Integral can be greatly enlarged. This method in conjunction with the finite element method (FEM) is employed to solve several representative fracture problems. According to the comparison between the results and those from the published lectures, good agreement demonstrates the validation of the interaction Integral. The results show that the present interaction Integral is Domain-independent for nonhomogeneous materials with interfaces.
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investigation of mixed mode stress intensity factors for nonhomogeneous materials using an interaction Integral method
International Journal of Solids and Structures, 2009Co-Authors: Licheng GuoAbstract:Abstract An interaction (energy) Integral is derived for the computation of mixed-mode stress intensity factors (SIFs) in nonhomogeneous materials with continuous or discontinuous properties. This method is based on a conservation Integral that relies on two admissible mechanical states (actual and auxiliary fields). In general, the interaction energy contour Integral is converted into an equivalent Domain Integral in numerical computations. It can be seen from the equivalent Domain Integral, the integrand does not involve any derivatives of material properties. Moreover, the formulation can be proved valid even when the Integral Domain contains material interfaces. Therefore, it is not necessary to limit the material properties to be continuous for the present method. Due to these advantages the application range of the interaction Integral method can be greatly enlarged. The numerical implementation of the derived expression is combined with the extended finite element method (XFEM). Using this method, the influences of material properties on the mixed-mode SIFs are investigated for four types of material properties selected in this work. Numerical results show that the mechanical properties and their first-order derivatives can affect mode I and II SIFs greatly, while the higher-order derivatives affect the SIFs very slightly.
Alan K Loper - One of the best experts on this subject based on the ideXlab platform.
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nagata rings kronecker function rings and related semistar operations
arXiv: Commutative Algebra, 2003Co-Authors: Marco Fontana, Alan K LoperAbstract:In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer's book \cite{G}) and, hence, the related classical theory of ideal systems based on the works by W. Krull, E. Noether, H. Pr\"{u}fer and P. Lorenzen from 1930's. In \cite{FL1} and \cite{FL2} the current authors investigated properties of the Kronecker function rings which arise from arbitrary semistar operations on an Integral Domain $D$. In this paper we extend that study and also generalize Kang's notion of a star Nagata ring \cite{Kang:1987} and \cite{Kang:1989} to the semistar setting. Our principal focuses are the similarities between the ideal structure of the Nagata and Kronecker semistar rings and between the natural semistar operations that these two types of function rings give rise to on $D$.
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nagata rings kronecker function rings and related semistar operations
Communications in Algebra, 2003Co-Authors: Marco Fontana, Alan K LoperAbstract:Abstract In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer's book (Gilmer, R. (1972). Multiplicative Ideal Theory. New York: Marcel Dekker) and, hence, the related classical theory of ideal systems based on the works by W. Krull, E. Noether, H. Prufer and P. Lorenzen from 1930's. Fontana and Loper investigated properties of the Kronecker function rings which arise from arbitrary semistar operations on an Integral Domain D (Fontana M., Loper K. A. (2001a). Kronecker function rings: a general approach. In Anderson, D. D., Papick, I. J., eds. Ideal Theoretic Methods in Commutative Algebra. Lecture Notes Pure Appl. Math. 220, Marcel Dekker, pp. 189–205 and Fontana, M., Loper, K. A. (2001b). A Krull-type theorem for the semistar Integral closure of an Integral Domain. ASJE Theme Issue “Commutative Algebra” 26:89–95). In this paper we extend that study and also generalize Kang's notion of a star Nagata r...