Clean coalgebras and clean comodules of finitely generated projective modules

N. P. Puspita ; I. E. Wijayanti ; B. Surodjo

Algebra and discrete mathematics, Tome 31 (2021) no. 2, pp. 251-260

Résumé

Let $R$ be a commutative ring with multiplicative identity and $P$ is a finitely generated projective $R$-module. If $P^{\ast}$ is the set of $R$-module homomorphism from $P$ to $R$, then the tensor product $P^{\ast}\otimes_{R}P$ can be considered as an $R$-coalgebra. Furthermore, $P$ and $P^{\ast}$ is a comodule over coalgebra $P^{\ast}\otimes_{R}P$. Using the Morita context, this paper give sufficient conditions of clean coalgebra $P^{\ast}\otimes_{R}P$ and clean $P^{\ast}\otimes_{R}P$-comodule $P$ and $P^{\ast}$. These sufficient conditions are determined by the conditions of module $P$ and ring $R$.

Détail

Keywords: clean coalgebra, clean comodule, finitely generated projective module
Mots-clés : Morita context.