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Abstract
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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.
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