Abstract
The paper is focused on questions when some homological and submodule-chain conditions satisfied by a module M are preserved by the group module MG. Namely, it is proved for a group G and an R-module M that MG(RG) is flat if and only if M-R is flat, and MG(RG) is artinian if and only if M-R is artinian and G is finite, which are two questions raised by Yiqiang Zhou: On Modules Over Group Rings, Noncommutative Rings and Their Applications LENS July 1-4, 2013.