Document Type : Original Manuscript

Authors

1 Faculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box 1561836314, Tehran, Iran.

2 Faculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box 1561836314, Tehran, Iran. Email: sayyarikh@gmail.

Abstract

Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered. Specially, we make some extensions and generalizations of a basic result of Peskine and Szpiro \cite[Proposition 1.3]{PS}, namely if $R$ is a Gorenstein local ring, $a \neq 0$ (an ideal of $R$) and $b := 0:_R a$ then $\frac{R}{a}$ is Cohen-Macaulay if and only if $\frac{R}{a}$ is unmixed and $\frac{R}{ b}$ is Cohen-Macaulay.

Keywords