This article is cited in 3 papers

Research articles

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

S. I. Bilavska, B. V. Zabavsky

Ivan Franko National University of Lviv, Lviv, Ukraine

Abstract: 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.

Keywords and phrases: almost prime ideal, completely prime ideal, $dr$-prime ideal, duo-element, finite element, finitely generated module, maximal non-finitely generated ideal.

MSC: 16D25, 16D80

Received: 02.03.2010

Language: English

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