Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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(𝓕, 𝓐)-GORENSTEIN FLAT HOMOLOGICAL DIMENSIONS

  • Becerril, Victor (Centro de Ciencias Matematicas Universidad Nacional Autonoma de Mexico)
  • Received : 2022.03.29
  • Accepted : 2022.07.15
  • Published : 2022.11.01
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Abstract

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(Rop) 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(Rop) × Mod(R) by the classes 𝓖𝓕(𝓕(Rop),𝓐) × 𝓖𝓕(𝓕(R),𝓐). When the duality pair is (𝓕(R), 𝓕𝓟Inj(Rop)) we recover the G. Yang's result over a Ding-Chen ring, and we see that is new for (Lev(R), AC(Rop)) among others.

Keywords

Acknowledgement

The author thanks to professors Marco A. Perez and Raymundo Bautista for suggestions and nice discussions about this paper.

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