关于极大内射性的注记(英文)  

Some Notes on Maximal Injectivity

作　　者：赵国[1] 汪明义[2] 

机构地区：[1]西南民族大学计算机科学与技术学院,成都610041 [2]四川师范大学数学研究所,成都610068

出　　处：《四川大学学报（自然科学版）》2005年第5期859-866,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省教育厅重点科研基金;四川省青年科学基金

摘　　要：环R上的右R-模E称为极大内射模,如果对每个极大右理想m,任何右R-模同态f:m→E都能扩张成右R-模同态f′:R→E.在本文中,作者应用极大内射模和函子Ext将内射维数推广到极大内射维数,并证明其为单模的投射维数的上确界.然后详细地考察了其特征模为极大内射模的一类模,揭示了这类模与关于Von Neumann正则环的Ramamurthi问题的内在联系,给出了关于Ramamurthi问题的部分结果.A right R-module E over a ring R is said to be maximally injective in ease for any maximal right ideal m of R , every R-homomorphism f： m→E can be extended to a R-homomorphism f′： R →E . In this paper, the authors first extend the conception of injective dimensions of any ring R to that of maximally injective dimensions, which turns out to be precisely the supremum of projective dimensions of simple R-modules. Then they investigate modules with maximally injective character modules, which has inherent connection with an famous open problem of Ramamurthi concerning Von Neumann regular rings. They end this paper with a partial affirmative answer to Ramarntlrthi’s problem under the right socular assumption.

关 键 词：自内射环 平坦模 Von Neumann正则环 

分 类 号：O153.3[理学—数学]