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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Alternative rings without nilpotent elements


Author: Irvin Roy Hentzel
Journal: Proc. Amer. Math. Soc. 42 (1974), 373-376
MSC: Primary 17D05
MathSciNet review: 0327858
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Abstract: In this paper we show that any alternative ring without nonzero nilpotent elements is a subdirect sum of alternative rings without zero divisors.

Andrunakievic and Rjabuhin proved the corresponding result for associative rings by a complicated$ ^{1}$ process in 1968. Our result extends Andrunakievic and Rjabuhin's result to the alternative case, and our argument is nearly as simple as in the associative-commutative case. Since right alternative rings of characteristic not 2 without nilpotent elements are alternative, our results extend to such rings as well.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0327858-3
PII: S 0002-9939(1974)0327858-3
Keywords: Nilpotent, zero divisor
Article copyright: © Copyright 1974 American Mathematical Society