Journal of the Australian Mathematical Society (Series A)
- Journal of the Australian Mathematical Society (Series A) / Volume 28 / Issue 03 / November 1979, pp 283-294
- Copyright © Australian Mathematical Society 1979
- DOI: http://dx.doi.org/10.1017/S1446788700012222 (About DOI), Published online: 09 April 2009
Research Article
Radicals related to the Brown-McCoy radical in some varieties of algebras
B. J. Gardnera1
a1 University of Tasmania Hobart, Australia
Abstract
The Brown-McCoy radical is the upper radical defined by the class of simple rings with identities. For associative or alternative rings the Brown-McCoy radical is hereditary, and its semi-simple class consists of all subdirect products of simple rings with identities. In this paper we present some classes of simple non-associative algebras whose upper radicals behave similarly. Classifications are then obtained of ‘most’ semi-simple radical classes of (γ, δ) and right alternative rings.
(Received November 16 1978)
(Revised April 04 1979)
1980 Mathematics subject classification (Amer. Math. Soc)
- 16 A 21;
- 17 A 30
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