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 - <p style="text-align: justify;">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.</p>