LINKAGE OF IDEALS OVER A MODULE

Jahangiri, M.; Sayyari, Kh.

doi:10.22044/jas.2020.9180.1447

LINKAGE OF IDEALS OVER A MODULE

Document Type : Original Manuscript

Authors

M. Jahangiri ¹
Kh. Sayyari ²

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.

10.22044/jas.2020.9180.1447

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