LINKAGE OF IDEALS OVER A MODULE

Classically, linkage theory refers to Halphen (1870) and M. Noether (1882) [9] who worked to classify space curves. In 1974, the significant work of Peskine and Szpiro [10] brought breakthrough to this theory and stated it in the modern algebraic language; two proper ideals a and b in a Cohen-Macaulay local ring R is said to be linked if there is a regular sequence x in their intersection such that a = x :R b and b = x :R a. A new progress in the linkage theory is the work of Martsinkovsky and Strooker [7] which established the concept of linkage of modules. Let R be a commutative Noetherian ring with 1 ̸= 0 and M be a finitely generated R-module. In this paper, inspired by the works in the ideal case, we present the concept of linkage of ideals over a module; let a, b and I ⊆ a ∩ b be ideals of R such that I is generated by an