Modules of Gorenstein dimension zero over graph algebras

2016 ◽  
Vol 207 (7) ◽  
pp. 964-982 ◽  
Author(s):  
E S Golod ◽  
G A Pogudin
Keyword(s):  
Graph Algebras ◽  
Dimension Zero ◽  
Gorenstein Dimension

scholarly journals On the category of modules of Gorenstein dimension zero II

2004 ◽  
Vol 278 (1) ◽  
pp. 402-410 ◽  
Author(s):  
Ryo Takahashi
Keyword(s):  
Dimension Zero ◽  
Gorenstein Dimension ◽  
Category Of Modules

On the category of modules of Gorenstein dimension zero

2005 ◽  
Vol 251 (2) ◽  
pp. 249-256 ◽  
Author(s):  
Ryo Takahashi
Keyword(s):  
Dimension Zero ◽  
Gorenstein Dimension ◽  
Category Of Modules

scholarly journals Associative spectra of graph algebras I

2021 ◽  
Author(s):  
Erkko Lehtonen ◽  
Tamás Waldhauser
Keyword(s):  
Catalan Numbers ◽  
Graph Algebras ◽  
Undirected Graphs ◽  
Powers Of 2

AbstractAssociative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities: constant 1, powers of 2, and Catalan numbers. Associative and antiassociative digraphs are described, and associative spectra are determined for certain families of digraphs, such as paths, cycles, and graphs on two vertices.

scholarly journals A generalization of the Auslander transpose and the generalized Gorenstein dimension

2013 ◽  
Vol 63 (1) ◽  
pp. 143-156 ◽  
Author(s):  
Yuxian Geng
Keyword(s):  
Gorenstein Dimension

Complete Intersection Flat Dimension and the Intersection Theorem

2012 ◽  
Vol 19 (spec01) ◽  
pp. 1161-1166
Author(s):  
Parviz Sahandi ◽  
Tirdad Sharif ◽  
Siamak Yassemi
Keyword(s):  
Local Ring ◽  
Complete Intersection ◽  
Intersection Theorem ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Gorenstein Dimension ◽  
Flat Dimension ◽  
Gorenstein Flat ◽  
Similar Extension

Any finitely generated module M over a local ring R is endowed with a complete intersection dimension CI-dim RM and a Gorenstein dimension G-dim RM. The Gorenstein dimension can be extended to all modules over the ring R. This paper presents a similar extension for the complete intersection dimension, and mentions the relation between this dimension and the Gorenstein flat dimension. In addition, we show that in the intersection theorem, the flat dimension can be replaced by the complete intersection flat dimension.

scholarly journals On approximate triangular decompositions in dimension zero

2007 ◽  
Vol 42 (7) ◽  
pp. 693-716 ◽  
Author(s):  
Marc Moreno Maza ◽  
Greg Reid ◽  
Robin Scott ◽  
Wenyuan Wu
Keyword(s):  
Dimension Zero

Free quotients of infinite rank of GL2 over Dedekind domains

1999 ◽  
Vol 129 (1) ◽  
pp. 77-84
Author(s):  
A. W. Mason
Keyword(s):  
Factor Group ◽  
Krull Dimension ◽  
Two Dimensional ◽  
Integral Domains ◽  
Dimension Zero ◽  
Infinite Rank ◽  
Dedekind Domains ◽  
Free Quotient

This paper is concerned with integral domains R, for which the factor group SL2(R)/U2(R) has a non-trivial, free quotient, where U2(R) is the subgroup of GL2(R) generated by the unipotent matrices. Recently, Krstić and McCool have proved that SL2(P[x])/U2(P[x]) has a free quotient of infinite rank, where P is a domain which is not a field. This extends earlier results of Grunewald, Mennicke and Vaserstein.Any ring of the type P[x] has Krull dimension at least 2. The purpose of this paper is to show that result of Krstić and McCool extends to some domains of Krull dimension 1, in particular to certain Dedekind domains. This result, which represents a two-dimensional anomaly is the best possible in the following sense. It is well known that SL2(R) = U2(R), when R is a domain of Krull dimension zero, i.e. when R is a field. It is already known that for some arithmetic Dedekind domains A, the factor group SL2(A)/U2(A) has a free quotient of finite (and not infinite) rank.

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