IMCS/Publications/BASM/Issues/BASM n.1 (65), 2011/

On the structure of maximal non-finitely generated ideals of ring and Cohen's theorem

Authors: S. I. Bilavska, B. V. Zabavsky


In this paper we consider analogues of Cohen's theorem. We introduce new notions of almost prime left (right) submodule and dr-prime left (right) ideal, this allows us to extend Cohen's theorem for modular and non-commutative analogues. We prove that if every almost prime submodule of a finitely generated module is a finitely generated submodule, then any submodule of this module is finitely generated.

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