Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-17T12:29:32.958Z Has data issue: false hasContentIssue false
  • English
  • Français

On rings generating atoms of lattices of special and supernilpotent radicals

Published online by Cambridge University Press:  17 April 2009

Halina France-Jackson
Halina France-Jackson
Affiliation:
Department of Mathematics, Vista University, Private Bag x613 Port Elizabeth 6000, South Africa
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.

This note is to indicate a nonsemiprime ring R such that the smallest supernilpotent (respectively special) radical containing the ring R is an atom of the lattice of all supernilpotent (respectively special) radicals. This gives a positive answer to Puczylowski's and Roszkowska's question.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 203 - 205
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Andrunakievich, V.A. and Rjabukhin, Yu. M., Radicals of Algebras and Structure Theory (Nauka, Moscow, 1979). (In Russian).Google Scholar
[2]France-Jackson, H., ‘*-rings and their radicals’, Questiones Math. 8 (1985), 231–239.CrossRefGoogle Scholar
[3]France-Jackson, H., ‘On atoms of the lattice of supernilpotent radicals’, Questiones Math. 10 (1987), 251–256.CrossRefGoogle Scholar
[4]Korolczuk, H., ‘A note on the lattice of special radicals’, Bull. Acad. Polon. Sci. Ser. Sci. Math. 29 (1981), 103–104.Google Scholar
[5]Puczylowski, E.R. and Roszkowska, E., ‘Atoms of lattices of radicals of associative rings’, Radical Theory, Proceedings of the 1988 Sendai Conference, 123–134.Google Scholar