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Rituparna Das - One of the best experts on this subject based on the ideXlab platform.
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Fine spectrum of the Upper Triangular Matrix U(r, 0, 0, s) over the sequence spaces c0 and c.
2018Co-Authors: Binod Chandra Tripathy, Rituparna DasAbstract:Fine spectra of various matrices have been examined by several authors. In this article we have determined the fine spectrum of the Upper Triangular Matrix U(r, 0, 0, s) on the sequence spaces c0 and c.
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On the spectrum and fine spectrum of the Upper Triangular Matrix \(U\left( r_1 ,r_2 ;s_1 ,s_2 \right) \) over the sequence space \(c_0 \)
2017Co-Authors: Rituparna DasAbstract:Several authors have determined spectra and fine spectra of different lower Triangular and Upper Triangular matrices over different sequence spaces with non-zero diagonals as entries of some constant sequences or some convergent sequences. In this article we determine the spectra and fine spectra of the Upper Triangular Matrix \(U\left( {r_1 ,r_2 ;s_1 ,s_2 } \right) \) over the sequence space \(c_0 \) where the non-zero diagonals are the entries of an oscillatory sequence.
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on the spectrum and fine spectrum of the Upper Triangular Matrix u left r_1 r_2 s_1 s_2 right over the sequence space c_0
Afrika Matematika, 2017Co-Authors: Rituparna DasAbstract:Several authors have determined spectra and fine spectra of different lower Triangular and Upper Triangular matrices over different sequence spaces with non-zero diagonals as entries of some constant sequences or some convergent sequences. In this article we determine the spectra and fine spectra of the Upper Triangular Matrix \(U\left( {r_1 ,r_2 ;s_1 ,s_2 } \right) \) over the sequence space \(c_0 \) where the non-zero diagonals are the entries of an oscillatory sequence.
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Spectrum and fine spectrum of the Upper Triangular Matrix U(r, s) over the sequence spaces
Proyecciones (Antofagasta), 2015Co-Authors: Binod Chandra Tripathy, Rituparna DasAbstract:Fine spectra of various Matrix operators on different sequence spaces have been investigated by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various Matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the Upper Triangular Matrix U(r,s) on the sequence space cs. In a further development, we have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator U(r,s) on the sequence space cs.
Wang Wen-kang - One of the best experts on this subject based on the ideXlab platform.
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Some skew McCoy subrings of Upper Triangular Matrix ring
Journal of Northwest University for Nationalities, 2010Co-Authors: Wang Wen-kangAbstract:Let σ be an endomorphism of ring R, be an extended endomorphism of ring Mn(R).A skew-McCoy subring of 3×3 Upper Triangular Matrix ring is found,an right skew-McCoy subring of 4×4 Upper Triangular Matrix ring is found,and a left skew-McCoy subring of 4×4 Upper Triangular Matrix ring is found.
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Armendariz and semicommutative properties of a class of Upper Triangular Matrix rings
Journal of Shandong University, 2008Co-Authors: Wang Wen-kangAbstract:A ring R is called Armendariz,if(∑mi=0aixi)(∑nj=0bjxj)=0∈R[x],then aibj=0,where 0≤i≤m,0≤j≤n.A ring R is called semicommutative if for any a,b∈R,ab=0 implies aRb=0.A ring is called reduced if it has no non-zero nilpotent elements.Every reduced ring is semicommutative.A class of Upper Triangular Matrix rings over-reduced rings is found to be both Armendariz and semicommutative.
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Armendariz Property of A Class of Upper Triangular Matrix Rings
Journal of Northwest University for Nationalities, 2007Co-Authors: Wang Wen-kangAbstract:Aring Ris called Armendariz,if∑mi =0aixi∑nj=0bjxj=0∈ R[ x],thenaibj=0,where 0≤i ≤ m,0≤j≤ n.Aring Ris called semicommutative,ifab=0,thenaRb=0,wherea,b∈ R.Let Rbe reduced,then a class of subringsWns(R)of Upper Triangular Matrix ring are Armendariz.
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Skew Armendariz Property of A Class of Upper Triangular Matrix Rings
Journal of Mathematical Research and Exposition, 2007Co-Authors: Wang Wen-kangAbstract:Letαbe an endomorphism of a ring R.A ring R is calledα-skew Armendariz,if(∑_(i=0)~m a_ix~i) (∑_(j=0)~n b_jx~j)=0 in R[x;α],then a_iα~i(b_j)=0,where 0■i■m,0■j■n.Let R beα-rigid.Then a class of subrings W_n(p,q)of Upper Triangular Matrix rings are■-skew Armendariz.
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Skew Armendariz property of a class of Upper Triangular Matrix rings
Journal of Northwest Normal University, 2006Co-Authors: Wang Wen-kangAbstract:Let α be an endomorphism of a ring R,and R be α-rigid ring.Then the subring W_n of Upper Triangular Matrix rings T_n(R) both is -skew Armendariz ring and Armendariz ring.
Daniel Maycock - One of the best experts on this subject based on the ideXlab platform.
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Derived Equivalences of Upper Triangular Differential Graded Algebras
Communications in Algebra, 2011Co-Authors: Daniel MaycockAbstract:This paper generalises a result for Upper Triangular Matrix rings to the situation of Upper Triangular Matrix differential graded algebras. An Upper Triangular Matrix DGA has the form (R, S, M) where R and S are differential graded algebras and M is a DG-left-R-right-S-bimodule. We show that under certain conditions on the DG-module M and with the existance of a DG-R-module X, from which we can build the derived category D(R), that there exists a derived equivalence between the Upper Triangular Matrix DGAs (R, S, M) and (S, M′, R′), where the DG-bimodule M′ is obtained from M and X and R′ is the endomorphism differential graded algebra of a K-projective resolution of X.
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Properties of Triangular Matrix and Gorenstein differential graded algebras
2011Co-Authors: Daniel MaycockAbstract:The main goal of this thesis is to investigate properties of two types of Differential Graded Algebras (or DGAs), namely Upper Triangular Matrix DGAs and Gorenstein DGAs. In doing so we extend a number of corresponding ring theory results to the more general setting of DGAs and DG modules. Chapters 2 and 3 contain background material. In chapter 2 we give a brief summary of some important aspects of homological algebra. Starting with the definition of an abelian category we give the construction of the derived category and the definition of derived functors. In chapter 3 we present the basics about Differential Graded Algebras and Differential Graded Modules in particular extending the definitions of the derived category and derived functors to the Differential Graded case before providing some results on Recollement of DGAs, Dualising DG-modules and Gorenstein DGAs. Chapters 4 and 5 contain the bulk of the work for the Thesis. In chapter 4 we look at Upper Triangular Matrix DGAs and in particular we generalise a result for Upper Triangular Matrix rings to the situation of Upper Triangular Matrix differential graded algebras. An Upper Triangular Matrix DGA has the form [ R M 0 S ] where R and S are DGAs and M is a DG R-Sop-bimodule. We show that under certain conditions on the DG-module M , and given the existence of a DG R-module X from which we can build the derived category D(R), that there exists a derived equivalence between the Upper Triangular Matrix DGAs [ R M 0 S ] and [ S M ′ 0 R′ ] , where the DG-bimodule M ′ is obtained from M and X, and R′ is the endomorphism differential graded algebra of a K-projective resolution of X. In chapter 5 we turn our attention to Gorenstein DGAs and generalise some results from Gorenstein rings to Gorenstein DGAs. We present a number of Gorenstein Theorems which state, for certain types of DGAs, that being Gorenstein is equivalent to the bounded and finite versions of the Auslander and Bass classes being maximal. We also provide a new definition of a Gorenstein morphism for DGAs by considering a DG bimodule as a generalised morphism of DGAs. We then show that some existing results for Gorenstein morphism extend to these “Generalised Gorenstein Morphisms”. We finally conclude with some examples of generalised Gorenstein morphisms for some well known DGAs.
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Derived Equivalences of Upper Triangular Differential Graded Algebras
arXiv: Rings and Algebras, 2009Co-Authors: Daniel MaycockAbstract:This paper generalises a result for Upper Triangular Matrix rings to the situation of Upper Triangular Matrix DGA's. An Upper Triangular Matrix DGA has the form (R,S,M) where R and S are differential graded algebras and M is a DG-left-R-right-S-bimodule. We show that under certain conditions on the DG-module M and with the existance of a DG-R-module X, from which we can build the derived category D(R), that there exists a derived equivalence between the Upper Triangular Matrix DGAs (R,S,M) and (S,M',R'), where the DG-bimodule M' is obtained from M and X and R' is the endomorphism DGA of a K-projective resolution of X.
Yu Wang - One of the best experts on this subject based on the ideXlab platform.
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the image of polynomials on 2 2 Upper Triangular Matrix algebras
Linear Algebra and its Applications, 2021Co-Authors: Yu Wang, Jia Zhou, Yingyu LuoAbstract:Abstract The goal of the paper is to give a complete description of the image of polynomials with zero constant term on 2 × 2 Upper Triangular Matrix algebras over an algebraically closed field.
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The image of polynomials on 2 × 2 Upper Triangular Matrix algebras
Linear Algebra and its Applications, 2021Co-Authors: Yu Wang, Jia Zhou, Yingyu LuoAbstract:Abstract The goal of the paper is to give a complete description of the image of polynomials with zero constant term on 2 × 2 Upper Triangular Matrix algebras over an algebraically closed field.
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The Images of Completely Homogeneous Polynomials on 2 × 2 Upper Triangular Matrix Algebras
Algebras and Representation Theory, 2020Co-Authors: Jia Zhou, Yu WangAbstract:The purpose of this paper is to initiate the study of the images of non-multilinear polynomials on Upper Triangular Matrix algebras. We shall give a complete description of the images of completely homogenous polynomials on 2 × 2 Upper Triangular Matrix algebras. As a consequence, we show that the image of some special completely homogenous polynomials on 2 × 2 Upper Triangular Matrix algebras are not vector spaces.
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the images of completely homogeneous polynomials on 2 2 Upper Triangular Matrix algebras
Algebras and Representation Theory, 2020Co-Authors: Jia Zhou, Yu WangAbstract:The purpose of this paper is to initiate the study of the images of non-multilinear polynomials on Upper Triangular Matrix algebras. We shall give a complete description of the images of completely homogenous polynomials on 2 × 2 Upper Triangular Matrix algebras. As a consequence, we show that the image of some special completely homogenous polynomials on 2 × 2 Upper Triangular Matrix algebras are not vector spaces.
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The images of multilinear polynomials on 2 × 2 Upper Triangular Matrix algebras
Linear & Multilinear Algebra, 2019Co-Authors: Yu WangAbstract:ABSTRACTThe purpose of this paper is to give a correct proof of a result on the images of non-commutative multilinear polynomials on 2×2 Upper Triangular Matrix algebra.
Thiago Castilho De Mello - One of the best experts on this subject based on the ideXlab platform.
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The image of multilinear polynomials evaluated on $3\times 3$ Upper Triangular matrices
arXiv: Rings and Algebras, 2019Co-Authors: Thiago Castilho De MelloAbstract:We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ Upper Triangular Matrix algebra over an infinite field.
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Images of multilinear polynomials of degree up to four on Upper Triangular matrices
Operators and Matrices, 2019Co-Authors: Pedro S. Fagundes, Thiago Castilho De MelloAbstract:We describe the images of multilinear polynomials of degree up to four on the Upper Triangular Matrix algebra.
