Some conditions for the existence of Gorenstein projective covers and preenvelopes

B Yu - Journal of Algebra and Its Applications, 2016 - World Scientific
Gorenstein projective modules is covering. We also characterize the rings over which the class
of Gorenstein projective modules … every module has a Gorenstein projective preenvelope. …

On Gorenstein injective modules

EE Enochs, OMG Jenda - Communications in Algebra, 1993 - Taylor & Francis
… 3 We first note that if Mv is Gorenstein projective, then Hom(E(k), M) = (Mu)* # 0 since MV #
0. … R-module N is Gorenstein projective if and only if N* is Gorenstein projective. Hence Mu is …

FPn-Injective, FPn-Flat Covers and Preenvelopes, and Gorenstein AC-Flat Covers

D Bravo, S Estrada, A Iacob - Algebra Colloquium, 2018 - World Scientific
… properties of Gorenstein flat modules extend to the class of Gorenstein AC-flat modules; for
Gorenstein flat modules) every Gorenstein AC-flat module is a direct summand of a strongly …

Stability of Gorenstein classes of modules

S Bouchiba - Algebra Colloquium, 2013 - World Scientific
… ) Gorenstein injective? We settle such a question in the affirmative and the dual result for the
Gorenstein projective modules … As an application, we provide the Gorenstein versions of the …

Gorenstein homological theory for differential modules

J Wei - Proceedings of the Royal Society of Edinburgh Section …, 2015 - cambridge.org
module is Gorenstein projective (injective, respectively) if and only if its underlying module is
Gorenstein projective (… We then relate the Ringel–Zhang theorem on differential modules to …

Finiteness criteria for Gorenstein flat dimension and stability

I Kaperonis, DD Stergiopoulou - Communications in Algebra, 2024 - Taylor & Francis
Gorenstein projective. While the relation between Gorenstein projective and Gorenstein flat
modules is not well understood, the class of projectively coresolved Gorenstein flat modules

On the finiteness of Gorenstein homological dimensions

I Emmanouil - Journal of Algebra, 2012 - Elsevier
… of modules of finite Gorenstein projective, injective and flat … all Gorenstein projective
modules are Gorenstein flat and … of the Gorenstein Tor-functor for modules of finite Gorenstein

Injective envelopes and (Gorenstein) flat covers

EE Enochs, Z Huang - Algebras and representation theory, 2012 - Springer
… envelopes of (Gorenstein) flat modules and (Gorenstein) flat covers of injective modules. We
… the injective envelope of R R is (Gorenstein) flat if and only if the injective envelope of every …

Tate homology of modules of finite Gorenstein flat dimension

L Liang - Algebras and Representation Theory, 2013 - Springer
… We notice that every (left or right) R-module over a Gorenstein ring R is of finite
Gorenstein flat dimension by [7, Theorem 12.3.1], and hence admits a Tate flat resolution. …

[HTML][HTML] Gorenstein conditions over triangular matrix rings

EE Enochs, M Cortés-Izurdiaga, B Torrecillas - Journal of Pure and Applied …, 2014 - Elsevier
Gorenstein projective modules) … Gorenstein projective modules over a left Gorenstein regular
ring R is a strong Kaplansky class, then so is the class of all Gorenstein projective modules