MMN-1283
Modules that have a supplement in every coatomic extension
Burcu Nişancı Türkmen;Abstract
Let R be a ring and M be an R-module. M is said to be an E* -module(respectively, an EE* -module) if M has a supplement (respectively, ample supplements) in every coatomic extension N, i.e. N/M is coatomic. We prove that if a module M is an EE* -module, every submodule of M is an E* -module, and then we show that a ring R is left perfect iff every left R-module is an E* -module iff every left R-module is an EE *-module. We also prove that the class of E *-modules is closed under extension. In addition, we give a new characterization of left V -rings by cofinitely injective modules.
Vol. 16 (2015), No. 1, pp. 543-551