The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ...

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 ...