Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T06:07:34.957Z Has data issue: false hasContentIssue false
  • English
  • Français

Complemented hereditary radicals

Published online by Cambridge University Press:  17 April 2009

Robert L. Snider
Robert L. Snider
Affiliation:
University of Miami, Coral Gables, Florida, USA.
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.

The complemented elements of the lattice of hereditary radicals are characterized. A hypernilpotent complemented hereditary radical is the upper radical determined by a finite number of finite matrix rings. As a corollary, Stewart's characterization of radical semisimple classes is obtained. The methods are universal algebraic in nature.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 3 , June 1971 , pp. 307 - 320
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Albert, A. Adrian, Structure of algebras (Colloquium Publ. 24, Amer. Math. Soc., New York, 1939).CrossRefGoogle Scholar
[2]Amitsur, S.A., “Associative rings with identities”, Some aspects of ring theory, ed. Herstein, I.N., (Centro Internazionalo Matematico Estivo, Roma, 1966).Google Scholar
[3]Amitsur, A.S. and Levitzki, J., “Minimal identities for algebras”, Proc. Amer. Math. Soc. 1 (1950), 449–463.CrossRefGoogle Scholar
[4]Andrunakievič, V.A., “Radicals of associative rings. I”, (Russian), Mat. Sb. N.S. 44 (86) (1958), 179–212.Google Scholar
[5]Arens, Richard F. and Kaplansky, Irving, “Topological representation of algebras”, Trans. Amer. Math. Soc. 63 (1948), 457–481.CrossRefGoogle Scholar
[6]Armendariz, E.P., “Closure properties in radical theory”, Pacific J. Math. 26 (1968), 1–7.CrossRefGoogle Scholar
[7]Divinsky, Nathan, Rings and radicals (University of Toronto Press, Toronto, 1965).Google Scholar
[8]Grätzer, George, Universal algebra (Van Nostrand, Princeton, New Jersey; Toronto; London; Melbourne; 1968).Google Scholar
[9]Kaplansky, Irving, “Rings with a polynomial identity”, Bull. Amer. Math. Soc. 54 (1948), 575–580.CrossRefGoogle Scholar
[10]Kaplansky, Irving, Topological representation of algebras. II”, Trans. Amer. Math. Soc. 68 (1950), 62–75.CrossRefGoogle Scholar
[11]Kuroš, A.G., “Radicals of rings and algebras”, (Russian), Mat. Sb. N.S. 33 (75) (1953), 13–26.Google Scholar
[12]Leron, U. and Vapne, A., “Polynomial identities of related rings”, Israel J. Math. 8 (1970), 127–137.CrossRefGoogle Scholar
[J3]Montgomery, M. Susan, “The Lie structure of simple rings with involution of characteristic 2”, (Ph.D. thesis, University of Chicago, Chicago, 1969).CrossRefGoogle Scholar
[14]Snider, Robert L., “Lattices of radicals”, (to appear).Google Scholar
[15]Stewart, Patrick N., “Semi-simple radical classes”, Pacific J. Math. 32 (1970), 249–254.CrossRefGoogle Scholar