Displaying similar documents to “A note on the countable union of prime submodules.”

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.

Prime and primary submodules of certain modules

A. Amini, B. Amini, Habib Sharif (2006)

Czechoslovak Mathematical Journal

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In this paper we characterize all prime and primary submodules of the free R -module R n for a principal ideal domain R and find the minimal primary decomposition of any submodule of R n . In the case n = 2 , we also determine the height of prime submodules.

On prime submodules and primary decomposition

Yücel Tiraş, Harmanci, Abdullah (2000)

Czechoslovak Mathematical Journal

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