نجمه دهقانی

For certain classes C of R-modules, including singular modules or modules with locally Krull dimensions, it is investigated when every module in C with a finitely generated essential submodule is finitely generated. In case C = Mod-R, this means E(M)/M is Noetherian for any finitely generated module M. Rings R with latter property are studied and shown that they form a class Q properly between the class of pure semisimple rings and the class of certain max rings. Duo rings in Q are precisely Artinian rings. If R is a quasi continuous ring in Q then R\simeq A\oplus T , where A is a semisimple Artinian ring and T\in Q with Z(T) is an essential submodule of T.