TY - JOUR ID - 1956 TI - LINKAGE OF IDEALS OVER A MODULE JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Jahangiri, M. AU - Sayyari, Kh. AD - Faculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box 1561836314, Tehran, Iran. AD - Faculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box 1561836314, Tehran, Iran. Email: sayyarikh@gmail. Y1 - 2021 PY - 2021 VL - 8 IS - 2 SP - 269 EP - 281 KW - Linkage of ideals KW - Cohen-Macaulay modules KW - canonical module DO - 10.22044/jas.2020.9180.1447 N2 - 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. UR - https://jas.shahroodut.ac.ir/article_1956.html L1 - https://jas.shahroodut.ac.ir/article_1956_05388a6d1c144832a0ff693aef3886a5.pdf ER -