Displaying similar documents to “A note on prime modules.”

On prime modules over pullback rings

Shahabaddin Ebrahimi Atani (2004)

Czechoslovak Mathematical Journal

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First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if R is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime R -modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.

Projective modules and prime submodules

Mustafa Alkan, Yücel Tiraş (2006)

Czechoslovak Mathematical Journal

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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.

The dual notion of prime submodules

Siamak Yassemi (2001)

Archivum Mathematicum

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In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced.