Volume 55, Issue 2
Gorenstein Hereditary Coalgebras

Yexuan Li & Hailou Yao

J. Math. Study, 55 (2022), pp. 216-228.

Published online: 2022-04

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  • 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.

  • AMS Subject Headings

16T15, 18G25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

leeyexuan@126.com (Yexuan Li)

yaohl@bjut.edu.cn (Hailou Yao)

  • BibTex
  • RIS
  • TXT
@Article{JMS-55-216, author = {Li , Yexuan and Yao , Hailou}, title = {Gorenstein Hereditary Coalgebras}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {55}, number = {2}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v55n2.22.08}, url = {http://global-sci.org/intro/article_detail/jms/20497.html} }
TY - JOUR T1 - Gorenstein Hereditary Coalgebras AU - Li , Yexuan AU - Yao , Hailou JO - Journal of Mathematical Study VL - 2 SP - 216 EP - 228 PY - 2022 DA - 2022/04 SN - 55 DO - http://doi.org/10.4208/jms.v55n2.22.08 UR - https://global-sci.org/intro/article_detail/jms/20497.html KW - Cosyzygy comodule, Gorenstein injective comodule, hereditary coalgebra, Gorenstein hereditary coalgebra. AB -

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.

Yexuan Li & Hailou Yao. (2022). Gorenstein Hereditary Coalgebras. Journal of Mathematical Study. 55 (2). 216-228. doi:10.4208/jms.v55n2.22.08
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