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Strongly Irreducible Submodules of Modules

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Abstract

Strongly irreducible submodules of modules are defined as follows: A submodule N of an R–module M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ⊆ N implies that either L ⊆ N or K ⊆ N. The relationship among the families of irreducible, strongly irreducible, prime and primary submodules of an R–module M is considered, and a characterization of Noetherian modules which contain a non-prime strongly irreducible submodule is given.

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  1. Department of Mathematics, Shiraz University, Shiraz, 71454, I. R. Iran

    A. Khaksari, M. Ershad & H. Sharif

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  1. A. Khaksari
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  2. M. Ershad
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  3. H. Sharif
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Correspondence to A. Khaksari.

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Khaksari, A., Ershad, M. & Sharif, H. Strongly Irreducible Submodules of Modules. Acta Math Sinica 22, 1189–1196 (2006). https://doi.org/10.1007/s10114-005-0681-7

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  • DOI: https://doi.org/10.1007/s10114-005-0681-7

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