Remarks on \(\alpha \)-strongly irreducible ideals (Q644531): Difference between revisions

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.