AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS

In this paper, a generalization of the integral depen-dence of rings on modules is given. The stability of the integral closure with respect to various module theoretic constructions isalso studied. Moreover, the notion of integral extension of a mod- ule is introduced, and the Lying over, Going up and Going down theorems for modules are proved.

کلیدواژه ها:

Prime submodule ، Integral element ، Integrally closed