Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T08:42:14.333Z Has data issue: false hasContentIssue false
  • English
  • Français

On semi-simple radical classes

Published online by Cambridge University Press:  17 April 2009

B.J. Gardner  and
Patrick N. Stewart
B.J. Gardner
Affiliation:
Department of Mathematics, University of Tasmania, Hobart, Tasmania;
Patrick N. Stewart
Affiliation:
Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, 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.

It has been incorrectly asserted that each non-trivial semi-simple radical class of associative rings is a variety defined by an equation of the form xn = x. In this paper we give, for each non-trivial semi-simple radical class of associative rings, a set of equations which does define that class as a variety.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 3 , December 1975 , pp. 349 - 353
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Gardner, B.J., “Semi-simple radical classes of algebras and attainability of identities”, submitted.Google Scholar
[2]van Leeuwen, L.C.A., “A note on primitive classes of rings”, submitted.Google Scholar
[3]Мартынов, Л.М. [Martynov, L.M.], “О разрешимых яолъцах” [On solvable rings], Ural. Gos. Univ. Mat. Zap. 8 (1972), tetrad' 3, 82–93.Google Scholar
[4]Michler, Gerhard und Wille, Rudolf, “Die primitiven Klassen arithmetis arithmetischer Ringe”, Math. Z. 113 (1970), 369–372.CrossRefGoogle Scholar
[5]Шеарин, Л.М. [Ševrin, L.N., Martynov, L.M.], “О достижимых классах алгебр” [On attainable classes of algebras], Sibirsk. Mat. Ž. 12 (1971), 1363–1381.Google Scholar
[6]Snider, Robert L., “Complemented hereditary radicals”, Bull. Austral. Math. Soc. 4 (1971), 307–320.CrossRefGoogle Scholar
[7]Stewart, Patrick N., “Semi-simple radical classes”, Pacific J. Math. 32 (1970), 249–254.CrossRefGoogle Scholar
[8]Werner, Heinrich und Wille, Rudolf, “Charakterisierungen der primitiven Klassen arithmetischer Ringe”, Math. Z. 115 (1970), 197–200.CrossRefGoogle Scholar
[9]Wiegandt, Richard, Radical and semisimple classes of rings (Queen's Papers in Pure and Applied Mathematics, 37. Queen's University, Kingston, Ontario, 1974).Google Scholar