Quasi-dual模和V-环的一个新的推广(英文)ON QUASI-DUAL MODULES AND A NEW GENERALIZATION OF V-RINGS
郭勇华,易忠
摘要(Abstract):
定义了quasi-dual模,讨论了它的性质和等价条件,并且通过quasi-dual模,详细讨论了V-环的一个新的推广结构,得到了以下等价条件:1R/Soc(RR)是右V-环;2每一个R的本质真右理想是极大右理想的交;3存在一个奇异半单右R-模是quasi-dual的.
关键词(KeyWords): quasi-dual环;V-环;零化子;奇异模
基金项目(Foundation): EYTPofMOEofChina(2002-40);; NSFofGuangxi(0135005,0447032);; GuangxiNormalUniversi-tyYouthResearchGrant
作者(Author): 郭勇华,易忠
参考文献(References):
- [1]Page S S,Zhou Y.Quasi-dual rings[J].Comm Algebra,2000,28(1):489—504.
- [2]Anderson F W,Fuller K R.Rings and categories of modules[M].Berlin:Springer-Verlag,1974.
- [3]Lam T Y.Lectures on modules and rings[M].Berlin:Springer-Verlag,1998.
- [4]李珊珊,汪明义.关于P-平坦模[J].广西师范大学学报(自然科学版),2004,22(4):36—40.
- [5]Ramamurthy V S,Rangaswamy K M.Generalised V-rings[J].Math Scandinavica,1972,31:69—77.
- [6]Varadarajan K.Generalised V-rings and torsion theories[J].Comm Algebra,1986,14(3):455—467.
- [7]Baccela G.Generalized V-rings and von Neumann regular rings[J].Rend Sem Mat Univ Padova,1984,72:117—133.
- [8]Tominaga H.On S-unital rings[J].Math J Okayama Univ,1976,18:117—133.
- [9]Yousif M F.V-modules with Krull dimension[J].Bull Austral Math Soc,1988,37:237—240.
- [10]Faith C,Menal P.A new duality theorem for semisimple modules and characterization of Villamayor rings[J].ProcAmer Math Soc,1995,123(6):1 635—1 637.
- [11]Boyle A K,Goodearl K R.Rings over which certain modules are injective[J].Pacific J Math,1975,58:43—53.
- [12]Gordon R,Robson J.Krull dimension[J].Mem Amer Math Soc,1973,133.
- [13]Chen J,Ding N.On regularity of rings[J].Algebra Colloquium,2001,8(3):267—274.