• Bulletin of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.173-187
• /
• 2014

In this article, we introduce and study the Gorenstein cotorsion dimension of modules and rings. It is shown that this dimension has nice properties when the ring in question is left GF-closed. The relations between the Gorenstein cotorsion dimension and other homological dimensions are discussed. Finally, we give some new characterizations of weak Gorenstein global dimension of coherent rings in terms of Gorenstein cotorsion modules.

• Journal of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1203-1227
• /
• 2022

In this paper we develop the homological properties of the Gorenstein (𝓛, 𝓐)-flat R-modules 𝓖𝓕_{(𝓕(R),𝓐)} proposed by Gillespie, where the class 𝓐 ⊆ Mod(R^op) sometimes corresponds to a duality pair (𝓛, 𝓐). We study the weak global and finitistic dimensions that come with the class 𝓖𝓕_{(𝓕(R),𝓐)} and show that over a (𝓛, 𝓐)-Gorenstein ring, the functor - ⊗_R - is left balanced over Mod(R^op) × Mod(R) by the classes 𝓖𝓕_{(𝓕(R^op),𝓐)} × 𝓖𝓕_{(𝓕(R),𝓐)}. When the duality pair is (𝓕(R), 𝓕𝓟Inj(R^op)) we recover the G. Yang's result over a Ding-Chen ring, and we see that is new for (Lev(R), AC(R^op)) among others.