Geodesic
On the structure of maximal non-finitely generated ideals of ring and Cohen's theorem
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2011), pp. 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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     author = {S. I. Bilavska and B. V. Zabavsky},
     title = {On the structure of maximal non-finitely generated ideals of ring and {Cohen's} theorem},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {33--41},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/BASM_2011_1_a2/}
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S. I. Bilavska; B. V. Zabavsky. On the structure of maximal non-finitely generated ideals of ring and Cohen's theorem. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2011), pp. 33-41. http://geodesic.mathdoc.fr/item/BASM_2011_1_a2/