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

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.

The paper defines the quasi-dual module,and discusses its characters and equivalent conditions. A new generalization of V-rings is given by terms of quasi-dual module. R/Soc（RR） is a right V-ring if and only if every proper essential right ideal E of R is an intersection of maximal right ideals ,if and only if there exists a singular semisimple right R-module which is quasi-dual.