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Article

Alkan, Mustafa ; Tiraş, Yücel
Projective modules and prime submodules. (English). Czechoslovak Mathematical Journal, vol. 56 (2006), issue 2, pp. 601-611
MSC: 13A10, 13A99, 13C10, 13C13 | MR 2291760 | Zbl 1155.13300
Keywords:
prime submodule; primary submodule; ${\scr S}$-closed subsets; the radical formula
Summary:
In this paper, we use Zorn’s Lemma, multiplicatively closed subsets and saturated closed subsets for the following two topics: (i) The existence of prime submodules in some cases, (ii) The proof that submodules with a certain property satisfy the radical formula. We also give a partial characterization of a submodule of a projective module which satisfies the prime property.
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