SOME NOTES ON MODULES IN WHICH ALL SUBMODULES HAVE A UNIQUE CLOSURE

摘要

A module M is called a UC-module if whenever every submodule of M has a unique closure. In this paper, we establish new characterizations of several well-studied classes of rings in terms of UC-modules, and show that UC is not a Morita invariant property. In addition, we study the behaviour of UC-modules under excellent extensions of rings. 2010 Mathematics Subject Classification: 16D10; 16D50