Strongly Irreducible Submodules of Modules  

作　　者：A.KHAKSARI M.ERSHAD H.SHARIF 

机构地区：[1]Department of Mathematics,Shiraz University Shiraz,71454,I.R.Iran

出　　处：《Acta Mathematica Sinica,English Series》2006年第4期1189-1196,共8页数学学报（英文版）

摘　　要：Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule 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.Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule 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.

关 键 词：irreducible and strongly irreducible module distributive module 

分 类 号：O153.3[理学—数学]