scholarly journals Gorenstein homological dimensions with respect to a semidualizing module

2018 ◽  
pp. 131-142 ◽  
Author(s):  
Zhen Zhang ◽  
Jiaqun Wei
Keyword(s):  
Semidualizing Module ◽  
Homological Dimensions

Homological Dimensions with Respect to a Semidualizing Module and Tensor Products of Algebras

2015 ◽  
Vol 22 (02) ◽  
pp. 215-222
Author(s):  
Maryam Salimi ◽  
Elham Tavasoli ◽  
Siamak Yassemi
Keyword(s):  
Commutative Ring ◽  
Noetherian Ring ◽  
Tensor Products ◽  
Projective Dimension ◽  
Injective Dimension ◽  
Semidualizing Module ◽  
Homological Dimensions

Let C be a semidualizing module for a commutative ring R. It is shown that the [Formula: see text]-injective dimension has the ability to detect the regularity of R as well as the [Formula: see text]-projective dimension. It is proved that if D is dualizing for a Noetherian ring R such that id R(D) = n < ∞, then [Formula: see text] for every flat R-module F. This extends the result due to Enochs and Jenda. Finally, over a Noetherian ring R, it is shown that if M is a pure submodule of an R-module N, then [Formula: see text]. This generalizes the result of Enochs and Holm.

Gorenstein Homological Dimensions of Complexes with Respect to a Semidualizing Module

2014 ◽  
Vol 42 (6) ◽  
pp. 2684-2703
Author(s):  
Chunxia Zhang ◽  
Limin Wang ◽  
Zhongkui Liu
Keyword(s):  
Semidualizing Module ◽  
Homological Dimensions

scholarly journals Gorenstein dimensions over some rings of the form R ⊕ C

2016 ◽  
Vol 15 (03) ◽  
pp. 1650043 ◽  
Author(s):  
Pye Phyo Aung
Keyword(s):  
Noetherian Ring ◽  
Local Cohomology ◽  
Positive Characteristic ◽  
Finiteness Condition ◽  
Trivial Extension ◽  
Commutative Noetherian Ring ◽  
Basic Properties ◽  
Semidualizing Module ◽  
Homological Dimensions ◽  
Amalgamated Duplication

Given a semidualizing module [Formula: see text] over a commutative Noetherian ring, Holm and Jørgensen [Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra 205(2) (2006) 423–445] investigate some connections between [Formula: see text]-Gorenstein dimensions of an [Formula: see text]-complex and Gorenstein dimensions of the same complex viewed as a complex over the “trivial extension” [Formula: see text]. We generalize some of their results to a certain type of retract diagram. We also investigate some examples of such retract diagrams, namely D’Anna and Fontana’s amalgamated duplication [An amalgamated duplication of a ring along an ideal: The basic properties, J. Algebra Appl. 6(3) (2007) 443–459] and Enescu’s pseudocanonical cover [A finiteness condition on local cohomology in positive characteristic, J. Pure Appl. Algebra 216(1) (2012) 115–118].

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

Homological Dimensions Relative to Special Subcategories

2021 ◽  
Vol 28 (01) ◽  
pp. 131-142
Author(s):  
Weiling Song ◽  
Tiwei Zhao ◽  
Zhaoyong Huang
Keyword(s):  
Abelian Category ◽  
Projective Dimension ◽  
Homological Dimensions ◽  
Category Of Modules ◽  
The Right

Let [Formula: see text] be an abelian category, [Formula: see text] an additive, full and self-orthogonal subcategory of [Formula: see text] closed under direct summands, [Formula: see text] the right Gorenstein subcategory of [Formula: see text] relative to [Formula: see text], and [Formula: see text] the left orthogonal class of [Formula: see text]. For an object [Formula: see text] in [Formula: see text], we prove that if [Formula: see text] is in the right 1-orthogonal class of [Formula: see text], then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Formula: see text] are identical; if the [Formula: see text]-projective dimension of [Formula: see text] is finite, then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Formula: see text] are identical. We also prove that the supremum of the [Formula: see text]-projective dimensions of objects with finite [Formula: see text]-projective dimension and that of the [Formula: see text]-projective dimensions of objects with finite [Formula: see text]-projective dimension coincide. Then we apply these results to the category of modules.

scholarly journals Homological dimensions and regular rings

2009 ◽  
Vol 322 (10) ◽  
pp. 3451-3458 ◽  
Author(s):  
Alina Iacob ◽  
Srikanth B. Iyengar
Keyword(s):  
Homological Dimensions ◽  
Regular Rings
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