F-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic p > 0

Abstract

Abstract: The main aim of this article is to study the relation between $ F $-injective singularity and the Frobenius closure of parameter ideals in Noetherian rings of positive characteristic. The paper consists of the following themes, including many other topics.\ begin {enumerate}\ item We prove that if every parameter ideal of a Noetherian local ring of prime characteristic $ p> 0$ is Frobenius closed, then it is $ F $-injective.