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| Strongly Irreducible Submodules of Modules | |
| 引用本文： | A. KHAKSARI M. ERSHAD H. SHARIF. Strongly Irreducible Submodules of Modules[J]. 数学学报(英文版), 2006, 22(4): 1189-1196. DOI: 10.1007/s10114-005-0681-7 |
| 作者姓名： | A. KHAKSARI M. ERSHAD H. SHARIF |
| 作者单位： | Department of Mathematics, Shiraz University Shiraz, 71454, I. R. Iran |
| 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. |
| 关 键 词： | 不可约 分布模式 子模 数学分析 |
| 收稿时间： | 2004-04-13 |
| 修稿时间： | 2004-04-132004-12-21 |
Strongly Irreducible Submodules of Modules |
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| A. Khaksari,M. Ershad,H. Sharif. Strongly Irreducible Submodules of Modules[J]. Acta Mathematica Sinica(English Series), 2006, 22(4): 1189-1196. DOI: 10.1007/s10114-005-0681-7 | |
| Authors: | A. Khaksari M. Ershad H. Sharif |
| Affiliation: | (1) Department of Mathematics, Shiraz University, Shiraz, 71454, I. R. Iran |
| 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. |
| Keywords: | irreducible and strongly irreducible module distributive module |
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