Year: 2022
Author: Meiqi Yan, Hailou Yao
Journal of Mathematical Study, Vol. 55 (2022), Iss. 2 : pp. 124–138
Abstract
In this paper, we introduce the Gorenstein hereditary and Gorenstein semi-hereditary modules and study the properties of the radical of Gorenstein projective modules over left artin rings. As an application, we characterize when Gorenstein projective modules are projective and give some characterizations of the Gorenstein hereditary rings by radical and Gorenstein projective modules over the endomorphism algebra of a module, respectively. Meanwhile we study the projective complexes over Gorenstein hereditary rings. In the last part of the paper, we study the heredity, Gorenstein heredity and quasi-heredity of the Morita context ring $\Lambda_{(0,0)}$ which is a left artin algebra.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v55n2.22.02
Journal of Mathematical Study, Vol. 55 (2022), Iss. 2 : pp. 124–138
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Gorenstein hereditary ring Gorenstein projective module radical projective complex Morita ring.