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Structure of pseudo-semisimple rings

Published online by Cambridge University Press:  09 April 2009

Saad Mohamed  and
Bruno J. Müller
Saad Mohamed
Affiliation:
Department of Mathematics Kuwait UniversityP.O. Box 5969Kuwait13060
Bruno J. Müller
Affiliation:
Department of Mathematics McMaster UniversityHamilton Ontario L8S 4K1, Canada
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Abstract

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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.

Keywords

16 A 42
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 1 , February 1991 , pp. 53 - 66
Copyright
Copyright © Australian Mathematical Society 1991

References

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