Projective modules and prime submodules. (English) Zbl 1155.13300

Summary: 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.


13A10 Radical theory on commutative rings (MSC2000)
13A99 General commutative ring theory
13C10 Projective and free modules and ideals in commutative rings
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