Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-03T15:12:38.662Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Golan, J. S., Localizations of non-commutative rings, (Marcel Dekker, 1975).Google Scholar
[2]Goodearl, K. R., Von Neumann regular rings, (Pitman, 1979).Google Scholar
[3]Mohamed, Saad and Müller, Bruno J., ‘Pseudo-semisimple rings’, Proc. Amer. Math. Soc. 85 (1982), 157–160.Google Scholar
[4]Mohamed, Saad and Singh, Surjeet, ‘Weak q-rings with zero singular ideals’, Proc. Amer. Math. Soc. 76 (1979), 25–30.Google Scholar
[5]Stenström, Bo, Rings of quotients, (Springer Verlag, 1975).CrossRefGoogle Scholar