The Experts below are selected from a list of 1908 Experts worldwide ranked by ideXlab platform
Alan E. Rubin - One of the best experts on this subject based on the ideXlab platform.
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edscottite fe5c2 a new iron carbide mineral from the ni rich Wedderburn iab iron meteorite
American Mineralogist, 2019Co-Authors: Alan E. RubinAbstract:Edscottite (IMA 2018-086a), Fe_5C_2, is a new iron carbide mineral that occurs with low-Ni iron (kamacite), taenite, nickelphosphide (Ni-dominant schreibersite), and minor cohenite in the Wedder-burn iron meteorite, a Ni-rich member of the group IAB complex. The mean chemical composition of edscottite determined by electron probe microanalysis, is (wt%) Fe 87.01, Ni 4.37, Co 0.82, C 7.90, total 100.10, yielding an empirical formula of (Fe_(4.73)Ni_(0.23)Co_(0.04))C_(2.00). The end-member formula is Fe_5C_2. Electron backscatter diffraction shows that edscottite has the C2/c Pd_5B_2-type structure of the synthetic phase called Hagg-carbide, χ-Fe_5C_2, which has a = 11.57 A, b= 4.57 A, c = 5.06 A, β = 97.7 °, V = 265.1 A^3, and Z = 4. The calculated density using the measured composition is 7.62 g/cm^3. Like the other two carbides found in iron meteorites, cohenite (Fe_3C) and haxonite (Fe_(23)C_6), edscottite forms in kamacite, but unlike these two carbides, it forms laths, possibly due to very rapid growth after supersaturation of carbon. Haxonite (which typically forms in carbide-bearing, Ni-rich members of the IAB complex) has not been observed in Wedderburn. Formation of edscottite rather than haxonite may have resulted from a lower C concentration in Wedderburn and hence a lower growth temperature. The new mineral is named in honor of Edward (Ed) R.D. Scott, a pioneering cosmochemist at the University of Hawai‘i at Manoa, for his seminal contributions to research on meteorites.
Emanuele Rodaro - One of the best experts on this subject based on the ideXlab platform.
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semisimple synchronizing automata and the Wedderburn artin theory
Developments in Language Theory, 2016Co-Authors: Jorge Almeida, Emanuele RodaroAbstract:We approach Cerný’s conjecture using the Wedderburn- Artin theory. We first introduce the radical ideal of a synchronizing automaton, and then the natural notion of semisimple synchronizing automata. This is a rather broad class since it contains simple synchronizing automata like those in Cerný’s series. Furthermore, semisimplicity gives the advantage of “factorizing” the problem of finding a synchronizing word into the sub-problems of finding words that are zeros in the projections into the simple components in the Wedderburn-Artin decomposition. This situation is applied to prove that Cerný’s conjecture holds for the class of strongly semisimple synchronizing automata. These are automata whose sets of synchronizing words are cyclic ideals, or equivalently are ideal regular languages which are closed by takings roots.
Jorge Almeida - One of the best experts on this subject based on the ideXlab platform.
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semisimple synchronizing automata and the Wedderburn artin theory
Developments in Language Theory, 2016Co-Authors: Jorge Almeida, Emanuele RodaroAbstract:We approach Cerný’s conjecture using the Wedderburn- Artin theory. We first introduce the radical ideal of a synchronizing automaton, and then the natural notion of semisimple synchronizing automata. This is a rather broad class since it contains simple synchronizing automata like those in Cerný’s series. Furthermore, semisimplicity gives the advantage of “factorizing” the problem of finding a synchronizing word into the sub-problems of finding words that are zeros in the projections into the simple components in the Wedderburn-Artin decomposition. This situation is applied to prove that Cerný’s conjecture holds for the class of strongly semisimple synchronizing automata. These are automata whose sets of synchronizing words are cyclic ideals, or equivalently are ideal regular languages which are closed by takings roots.
M. R. Vedadi - One of the best experts on this subject based on the ideXlab platform.
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several generalizations of the Wedderburn artin theorem with applications
Algebras and Representation Theory, 2018Co-Authors: Mahmood Behboodi, Asghar Daneshvar, M. R. VedadiAbstract:We say that an R-module M is virtually semisimple if each submodule of M is isomorphic to a direct summand of M. A nonzero indecomposable virtually semisimple module is then called a virtually simple module. We carry out a study of virtually semisimple modules and modules which are direct sums of virtually simple modules . Our study provides several natural generalizations of the Wedderburn-Artin Theorem and an analogous to the classical Krull-Schmidt Theorem. Some applications of these theorems are indicated. For instance, it is shown that the following statements are equivalent for a ring R: (i) Every finitely generated left (right) R-module is virtually semisimple; (ii) Every finitely generated left (right) R-module is a direct sum of virtually simple R-modules; (iii) $R\cong {\prod }_{i = 1}^{k} M_{n_{i}}(D_{i})$ where k,n 1,…,n k ∈ ℕ and each D i is a principal ideal V-domain; and (iv) Every nonzero finitely generated left R-module can be written uniquely (up to isomorphism and order of the factors) in the form R m 1 ⊕… ⊕ R m k where each R m i is either a simple R-module or a virtually simple direct summand of R.
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virtually semisimple modules and a generalization of the Wedderburn artin theorem
Communications in Algebra, 2018Co-Authors: Mahmood Behboodi, Asghar Daneshvar, M. R. VedadiAbstract:ABSTRACTA widely used result of Wedderburn and Artin states that “every left ideal of a ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct product of matrix rings over division rings.” Motivated by this, we call a module M virtually semisimple if every submodule of M is isomorphic to a direct summand of M and M is called completely virtually semisimple if every submodule of M is virtually semisimple. We show that the left R-module R is completely virtually semisimple if and only if R has a unique decomposition as a finite direct product of matrix rings over principal left ideal domains. This shows that R is completely virtually semisimple on both sides if and only if every finitely generated (left and right) R-module is a direct sum of a singular module and a projective virtually semisimple module. The Wedderburn-Artin theorem follows as a corollary from our result.
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virtually semisimple modules and a generalization of the Wedderburn artin theorem
Communications in Algebra, 2018Co-Authors: Mahmood Behboodi, Asghar Daneshvar, M. R. VedadiAbstract:ABSTRACTA widely used result of Wedderburn and Artin states that “every left ideal of a ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct product of mat...
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Virtually Semisimple Modules and a Generalization of the Wedderburn-Artin Theorem
arXiv: Rings and Algebras, 2016Co-Authors: Mahmood Behboodi, Asghar Daneshvar, M. R. VedadiAbstract:By any measure, semisimple modules form one of the most important classes of modules and play a distinguished role in the module theory and its applications. One of the most fundamental results in this area is the Wedderburn-Artin theorem. In this paper, we establish natural generalizations of semisimple modules and give a generalization of the Wedderburn-Artin theorem. We study modules in which every submodule is isomorphic to a direct summand and name them {\it virtually semisimple modules}. A module $_RM$ is called {\it completely virtually semisimple} if each submodules of $M$ is a virtually semisimple module. A ring $R$ is then called {\it left} ({\it completely}) {\it virtually semisimple} if $_RR$ is a left (compleatly) virtually semisimple $R$-module. Among other things, we give several characterizations of left (completely) virtually semisimple rings. For instance, it is shown that a ring $R$ is left completely virtually semisimple if and only if $R \cong \prod _{i=1}^ k M_{n_i}(D_i)$ where $k, n_1, ...,n_k\in \Bbb{N}$ and each $D_i$ is a principal left ideal domain. Moreover, the integers $k,~ n_1, ...,n_k$ and the principal left ideal domains $D_1, ...,D_k$ are uniquely determined (up to isomorphism) by $R$.
Angel Del Rio - One of the best experts on this subject based on the ideXlab platform.
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an algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the gap package wedderga
Journal of Symbolic Computation, 2009Co-Authors: Gabriela Olteanu, Angel Del RioAbstract:We present an algorithm to compute the Wedderburn decomposition of semisimple group algebras based on a computational approach of the Brauer-Witt theorem. The algorithm was implemented in the GAP package wedderga.
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Wedderburn decomposition of finite group algebras
Finite Fields and Their Applications, 2007Co-Authors: Osnel Broche, Angel Del RioAbstract:We show a method to effectively compute the Wedderburn decomposition and the primitive central idempotents of a semisimple finite group algebra of an abelian-by-supersolvable group G from certain pairs of subgroups of G.
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on monomial characters and central idempotents of rational group algebras
Communications in Algebra, 2004Co-Authors: Aurora Olivieri, Angel Del Rio, Juan Jacobo SimonAbstract:Abstract We give a method to obtain the primitive central idempotent of the rational group algebra ℚG over a finite group G associated to a monomial irreducible character which does not involve computations with the character field nor its Galois group. We also show that for abelian-by-supersolvable groups this method takes a particularly easy form that can be used to compute the Wedderburn decomposition of ℚG.
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an algorithm to compute the primitive central idempotents and the Wedderburn decomposition of a rational group algebra
Journal of Symbolic Computation, 2003Co-Authors: Aurora Olivieri, Angel Del RioAbstract:We present an algorithm to compute the primitive central idempotents and the Wedderburn decomposition of a rational group algebra. This algorithm has been implemented for System GAP, version 4.
