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On endomorphisms of multiplication and comultiplication modules

H. Ansari-Toroghy, F. Farshadifar (2008)

Archivum Mathematicum

Let R be a ring with an identity (not necessarily commutative) and let M be a left R -module. This paper deals with multiplication and comultiplication left R -modules M having right End R ( M ) -module structures.

On finitely generated multiplication modules

R. Nekooei (2005)

Czechoslovak Mathematical Journal

We shall prove that if M is a finitely generated multiplication module and A n n ( M ) is a finitely generated ideal of R , then there exists a distributive lattice M ¯ such that S p e c ( M ) with Zariski topology is homeomorphic to S p e c ( M ¯ ) to Stone topology. Finally we shall give a characterization of finitely generated multiplication R -modules M such that A n n ( M ) is a finitely generated ideal of R .

On prime submodules and primary decomposition

Yücel Tiraş, Harmanci, Abdullah (2000)

Czechoslovak Mathematical Journal

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 .

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