Structure of pseudo-semisimple rings

Journal of the Australian Mathematical Society

Saad Mohamed¹ 

[1] Bruno J. Müller

关键词: primary 16 A 48;    secondary 16 A 42;    16 A 42;    16 A 52;   

DOI  :  10.1017/S1446788700032547

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

A ring R is called right pseudo-semisimple if every right ideal not isomorphic to R is semisimpie. Rings of this type in which the right socle S splits off additively were characterized; such a ring has S2 = 0. The existence of right pseudo-semisimple rings with zero right singular ideal Z remained open, except for the trivial examples of semisimple rings and principal right ideal domains. In this work we give a complete characterization of right pseudo-semisimple rings with S2 = 0. We also give examples of non-trivial right pseudo-semisimple rings with Z = 0; in fact it is shown that such rings exist as subrings in every infinite-dimensional full linear ring. A structure theorem for non-singular right pseudo-semisimple rings, with homogeneous maximal socle, is given. The general case is still open.

【 授权许可】

Unknown