| Conţinutul numărului revistei |
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 SM ISO690:2012BILAVSKA, S, ZABAVSKI, B. On the structure of maximal non-finitely generated ideals of ring and Cohen’s theorem. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2011, nr. 1(65), pp. 33-41. ISSN 1024-7696. |
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 Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica |
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| Numărul 1(65) / 2011 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 33-41 | ||||||
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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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| Cuvinte-cheie Almost prime ideal, dr-prime ideal, duo-element, finite element, completely prime ideal |
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