Alternative rings without nilpotent elements

Hentzel, Irvin Roy

doi:10.1090/S0002-9939-1974-0327858-3

Alternative rings without nilpotent elements
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by Irvin Roy Hentzel PDF

Proc. Amer. Math. Soc. 42 (1974), 373-376 Request permission

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.

References

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