| 伪内射模与特殊环 |
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| 引用本文： | 班秀和,韦儒和.伪内射模与特殊环[J].阜阳师范学院学报(自然科学版),2008,25(2):12-14. |
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| 作者姓名： | 班秀和 韦儒和 |
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| 作者单位： | 广西师范学院,数学与计算机科学系,广西,南宁,530001 |
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| 摘 要： | 研究了伪内射模的性质，用伪内射模刻画了半单环，Noether、V-环，半Artin环和半局部环，得到的主要结果为：（1）伪内射模的完全不变子模是伪内射模；（2）尺是半单环当且仅当伪内射模与半单模一致当且仅当半本原模是伪内射模，且本质基座的模是伪内射模当且仅当基座为0的模是伪内射模，伪内射模的直和伪内射；（3）尺半Artin环当且仅当基座为0的模伪内射；（4）尺是半局部环当且仅当尺为左良好环且半本原模是伪内射模．
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| 关 键 词： | 伪内射模 半单环 Noether V-环 半Artin环 半局部环 |
Pseudo-injective Modules and Special Rings |
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| BAN Xiu-he,WEI Ru-he.Pseudo-injective Modules and Special Rings[J].Journal of Fuyang Teachers College:Natural Science,2008,25(2):12-14. |
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| Authors: | BAN Xiu-he WEI Ru-he |
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| Institution: | BAN Xiu-he,WEI Ru-he(Department of Mathematics , Computer Science,Guangxi Teachers college,Nanning Jiangsu 530001,China) |
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| Abstract: | In this paper,two properties of pseudo-injective modules are obtained.And semi-simple rings,Noetherian,V-rings,semi-Artinian rings,semi-local rings are characterized by pseudo-injective modules.The main results as follows :(1) The fully invariant submodules of a pseudo-injective module are pseudo-injective;(2) R is a semi-simple ring iff pseudo-injective modules are coincident with semi-simple modules iff every semiprimitive module is pseudo-injective,and every module that its socle is essential in it is ps... |
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| Keywords: | pseudo-injective module semi-simple ring noetherian、v-ring semi-artinian ring semi-local ring |
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