Absolutely clean, level, and Gorenstein AC-injective complexes
D Bravo, J Gillespie - Communications in Algebra, 2016 - Taylor & Francis
Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …
homological algebra can be extended to an arbitrary ring R. This led to the notion of …
Gorenstein AC-projective complexes
J Gillespie - Journal of Homotopy and Related Structures, 2018 - Springer
Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …
AC-Gorenstein rings and their stable module categories
J Gillespie - Journal of the Australian Mathematical Society, 2019 - cambridge.org
We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of
Gorenstein ring that is compatible with the Gorenstein AC-injective and Gorenstein AC …
Gorenstein ring that is compatible with the Gorenstein AC-injective and Gorenstein AC …
[PDF][PDF] A brief introduction to Gorenstein projective modules
P Zhang - Notes https://www. math. uni-bielefeld. de/~ sek/sem …, 2008 - Citeseer
Since Eilenberg and Moore [EM], the relative homological algebra, especially the
Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The …
Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The …
Generalized Gorenstein modules
A Iacob - Algebra Colloquium, 2022 - World Scientific
We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …
[HTML][HTML] Gorenstein-projective modules and symmetric recollements
P Zhang - Journal of Algebra, 2013 - Elsevier
We introduce compatible bimodules. If M is a compatible A–B-bimodule, then the Gorenstein-
projective modules over algebra Λ=(AM0B) are explicitly described; and if Λ is Gorenstein …
projective modules over algebra Λ=(AM0B) are explicitly described; and if Λ is Gorenstein …
Gorenstein model structures and generalized derived categories
J Gillespie, M Hovey - Proceedings of the Edinburgh Mathematical …, 2010 - cambridge.org
In a paper from 2002, Hovey introduced the Gorenstein projective and Gorenstein injective
model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring …
model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring …
Locally type and -coherent categories
D Bravo, J Gillespie, MA Pérez - arXiv preprint arXiv:1908.10987, 2019 - arxiv.org
We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …
[HTML][HTML] The flat stable module category of a coherent ring
J Gillespie - Journal of Pure and Applied Algebra, 2017 - Elsevier
Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …
Gorenstein injective and projective complexes
EE Enochs, JR Garcí Rozas - Communications in Algebra, 1998 - Taylor & Francis
In this article we extend the notion of Gorenstein injective and projective modules to that of
complexes and characterize such complexes. We prove that over an n-Gorenstein ring every …
complexes and characterize such complexes. We prove that over an n-Gorenstein ring every …