Year: 2022
Author: Yexuan Li, Hailou Yao
Journal of Mathematical Study, Vol. 55 (2022), Iss. 2 : pp. 216–228
Abstract
Let $C$ be a coalgebra. We prove that a right $C$-comodule is an $n$-cosyzygy if and only if it is a Gorenstein $n$-cosyzygy. We study the Gorenstein global dimension of coalgebras and the class of Gorenstein hereditary coalgebras. As a generalization of Gorenstein hereditary coalgebras, we introduce the concept of Gorenstein semihereditary coalgebras and show that a coalgebra $C$ is Gorenstein semihereditary if and only if every finitely cogenerated factor of any injective comodule is Gorenstein injective.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v55n2.22.08
Journal of Mathematical Study, Vol. 55 (2022), Iss. 2 : pp. 216–228
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Cosyzygy comodule Gorenstein injective comodule hereditary coalgebra Gorenstein hereditary coalgebra.