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On syzygy modules for polynomial matrices
 LINEAR ALGEBRA AND ITS APPLICATIONS 298 (1999) 73–86
, 1999
"... In this paper, we apply the theory of multivariate polynomial matrices to the study of syzygy modules for a system of homogeneous linear equations with multivariate polynomial coefficients. Several interesting structural properties of syzygy modules are presented and ..."
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Cited by 4 (1 self)
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In this paper, we apply the theory of multivariate polynomial matrices to the study of syzygy modules for a system of homogeneous linear equations with multivariate polynomial coefficients. Several interesting structural properties of syzygy modules are presented and
Gorenstein Syzygy Modules
, 2009
"... For any ring R and any positive integer n, we prove that a left Rmodule is a Gorenstein nsyzygy if and only if it is an nsyzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of finitely generated modules. We prove that a module M ∈ mod R op is a Goren ..."
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Cited by 2 (0 self)
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For any ring R and any positive integer n, we prove that a left Rmodule is a Gorenstein nsyzygy if and only if it is an nsyzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of finitely generated modules. We prove that a module M ∈ mod R op is a
Syzygy modules with semidualizing or Gprojective summands
 J. Algebra
"... Abstract. Let R be a commutative Noetherian local ring with residue class field k. In this paper, we mainly investigate direct summands of the syzygy modules of k. We prove that R is regular if and only if some syzygy module of k has a semidualizing summand. After that, we consider whether R is Gore ..."
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Abstract. Let R be a commutative Noetherian local ring with residue class field k. In this paper, we mainly investigate direct summands of the syzygy modules of k. We prove that R is regular if and only if some syzygy module of k has a semidualizing summand. After that, we consider whether R
Syzygy modules for quasi kGorenstein rings
, 2004
"... Let Λ be a quasi kGorenstein ring. For each dth syzygy module M in mod Λ (where 0 ≤ d ≤ k − 1), we obtain an exact sequence 0 → B → M ⊕ P → C → 0 in mod Λ with the properties that it is dual exact, P is projective, C is a (d + 1)st syzygy module, B is a dth syzygy of Ext d+1 Λ (D(M), Λ) and the rig ..."
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Let Λ be a quasi kGorenstein ring. For each dth syzygy module M in mod Λ (where 0 ≤ d ≤ k − 1), we obtain an exact sequence 0 → B → M ⊕ P → C → 0 in mod Λ with the properties that it is dual exact, P is projective, C is a (d + 1)st syzygy module, B is a dth syzygy of Ext d+1 Λ (D(M), Λ
Direct summands of syzygy modules of the residue class field
"... Abstract. Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the nth syzygy module of the residue class field of R has a nontrivial direct summand of finite Gdimension for some n. It is proved that if n is at most two then it is true, ..."
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Abstract. Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the nth syzygy module of the residue class field of R has a nontrivial direct summand of finite Gdimension for some n. It is proved that if n is at most two then it is true
Graphs, Syzygies and Multivariate Splines
, 2004
"... The module of splines on a polyhedral complex can be viewed as the syzygy module of its dual graph with edges weighted by powers of linear forms. When the assignment of linear forms to edges meets certain conditions, we can decompose the graph into disjoint cycles without changing the isomorphism cl ..."
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The module of splines on a polyhedral complex can be viewed as the syzygy module of its dual graph with edges weighted by powers of linear forms. When the assignment of linear forms to edges meets certain conditions, we can decompose the graph into disjoint cycles without changing the isomorphism
Relative Syzygies and Grade of Modules
"... Abstract Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslander and Bridger and the Cohen–Macaulay approximation theorem due to Auslander and Buchweitz. In this p ..."
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Abstract Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslander and Bridger and the Cohen–Macaulay approximation theorem due to Auslander and Buchweitz
Results 1  10
of
121