Somayeh Karimzadeh

[ 1 ] - AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS

In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.