LINKAGE OF IDEALS OVER A MODULE

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 [10, proposition 1.3], namely if r is a gorenstein local ring, a ̸= 0 (an ideal of r) and b := 0 :r a then r /a is cohen-macaulay if and only if r/ a is unmixed and r/ b is cohen-macaulay.