Prime and primary submodules of certain modules

A. Amini; B. Amini; Habib Sharif

Displaying similar documents to “Prime and primary submodules of certain modules”

On prime submodules and primary decomposition

Yücel Tiraş, Harmanci, Abdullah (2000)

Czechoslovak Mathematical Journal

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We characterize prime submodules of $R \times R$ for a principal ideal domain $R$ and investigate the primary decomposition of any submodule into primary submodules of $R \times R .$

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.

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.