Remarks on \(\alpha \)-strongly irreducible ideals (Q644531)
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scientific article; zbMATH DE number 5968165
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Remarks on \(\alpha \)-strongly irreducible ideals |
scientific article; zbMATH DE number 5968165 |
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Remarks on \(\alpha \)-strongly irreducible ideals (English)
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4 November 2011
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In the paper under review, the authors find some results on the notion of \(\alpha \)-strongly irreduciblility introduced by \textit{X. Lu} and \textit{H. Qin} [Southeast Asian Bull. Math. 32, No. 2, 299--303 (2008; Zbl 1174.13005)]. It is proved that a submodule \(N\) of a multiplication module \(M\) is an \(\alpha \)-strongly irreducible submodule iff its colon ideal is an \(\alpha \)-strongly irreducible ideal. Also, this concept is considered in the localization construction.
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\(\alpha \)-irreducible
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\(\alpha \)-strongly irreducible
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ideal
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faithful module
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multiplication module
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