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Ding projective dimension of Gorenstein flat modules

Junpeng Wang
대한수학회 (The Korean Mathematical Society)|2017.11|대한수학회보 (Bulletin of the KMS)|제54권 제6호|pp. 1935-1950

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키워드

Ding projective moduleGorenstein flat moduleDing-Chen ring
주제분류수학

초록

Let $R$ be a Ding-Chen ring. Yang \cite{Yang2012} and Zhang \cite{Zhang2015} asked whether or not every $R$-module has finite Ding projective or Ding injective dimension. In this paper, we give a new characterization of that all modul\-es have finite Ding projective and Ding injective dimension in terms of the relationship between Ding projective and Gorenstein flat modules. We also give an example to obtain negative answer to the above question.

Abstract

Let $R$ be a Ding-Chen ring. Yang \cite{Yang2012} and Zhang \cite{Zhang2015} asked whether or not every $R$-module has finite Ding projective or Ding injective dimension. In this paper, we give a new characterization of that all modul\-es have finite Ding projective and Ding injective dimension in terms of the relationship between Ding projective and Gorenstein flat modules. We also give an example to obtain negative answer to the above question.

참고문헌 (25)

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관련 논문AI추천

Homological properties of modules over Ding-Chen ringsGang Yang대한수학회 · 대한수학회지2012 · 제49권 제1호Ding projective modules with respect to a semidualizing moduleChunxia Zhang, Limin Wang, Zhongkui Liu대한수학회 · 대한수학회보2014 · 제51권 제2호$(\Flat, \A)$-Gorenstein flat homological dimensionsVictor Becerril대한수학회 · 대한수학회지2022 · 제59권 제6호THE DIMENSIONS OF GORENSTEIN XY-FLAT MODULES WITH RESPECT TO A SEMIDUALIZING MODULESA. UMAMAHESWARAN, M. PARIMALA, R. UDHAYAKUMAR, V. BIJU장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제4호ON n-STRONGLY E-GORENSTEIN INJECTIVE AND FLAT MODULESWei Zhao, Zenghui Gao대한수학회 · 대한수학회지2024 · 제61권 제6호On GI-flat modules and dimensionsZenghui Gao대한수학회 · 대한수학회지2013 · 제50권 제1호

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