Shahrood University of TechnologyJournal of Algebraic Systems2345-51288220210101LINKAGE OF IDEALS OVER A MODULE269281195610.22044/jas.2020.9180.1447ENM. JahangiriFaculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box
1561836314, Tehran, Iran.Kh. SayyariFaculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box
1561836314, Tehran, Iran.
Email: sayyarikh@gmail.Journal Article20191211Inspired 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.https://jas.shahroodut.ac.ir/article_1956_05388a6d1c144832a0ff693aef3886a5.pdf