A characterization of uniserial rings via continuous and discrete modules

Journal of the Australian Mathematical Society

S. K. Jain¹ 

[1] S. R. Lopez-Permouth

关键词: 16 A 35;    16 A 36;    16 A 50;    16 A 51;    16 A 52;   

DOI  :  10.1017/S1446788700032687

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

It is well-known that quasi-Frobenius rings are characterized by the property that all propective right modules are injective, as well as by the property that all injective right modules are projective. Similarly, either the property that every quasi-injective or that every quasi-injective is quasi-projective characterizes uniserial rings. Oshiro has given similar characterizations for generalized uniserial rings. The purpose of this paper is to characterize rings for which continuous right modules are discrete. We show that these rings are precisely the uniserial rings. The property that every discrete module is continuous is also investigated.

【 授权许可】

Unknown