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Lower radicals in nonassociative rings

Published online by Cambridge University Press:  09 April 2009

R. Tangeman  and
D. Kreiling
R. Tangeman
Affiliation:
University of Florida Western Illinois UniversityMacomb, Illinois 61455 U.S.A.
D. Kreiling
Affiliation:
University of Florida Western Illinois UniversityMacomb, Illinois 61455 U.S.A.
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Let W be a universal class of (not necessarily associative) rings and let A ⊆ W. Kurosh has given in [6] a construction for LA, the lower radical class determined by A in W. Using this construction, Leavitt and Hoffmann have proved in [4] that if A is a hereditary class (if K ∈ A and I is an ideal of K, then I ∈ A), then LA is also hereditary. In this paper an alternate lower radical construction is given. As applications, a simple proof is given of the theorem of Leavitt and Hoffmann and a result of Yu-Lee Lee for alternative rings is extended to not necessarily associative rings.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 4 , December 1972 , pp. 419 - 423
Copyright
Copyright © Australian Mathematical Society 1972

References

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