J Austral Math Soc Ser A 50 pp53--66, 1991.

Structure of Pseudo-Semisimple Rings

Saad Mohamed and Bruno J. Müller

(Received 2 May 1989; revised 10 October 1989)

Abstract

A ring R is called right pseudo-semisimple of every right ideal not isomorphic to R is semisimple. 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 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 homogenous maximal socle, is given. The general case is still open.

1980 AMS Subject Classification (1985 Revision): primary 16A48; secondary 16A42, 16A52

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Authors

Saad Mohamed: Department of Mathematics, Kuwait University, P.O. Box 5969, Kuwait 13060.
Bruno J. Müller: Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada.

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Last Modified: Mon Feb 3 9:46:10 2003