Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on generalizing alternative rings


Authors: Irvin Roy Hentzel and Giulia Maria Piacentini Cattaneo
Journal: Proc. Amer. Math. Soc. 55 (1976), 6-8
DOI: https://doi.org/10.1090/S0002-9939-1976-0393157-9
MathSciNet review: 0393157
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: Let $ R$ be a nonassociative ring of characteristic different from $ 2$ and $ 3$ which satisfies the following identities:

$\displaystyle ({\text{i)}}\;(ab,c,d) + (a,b,[c,d]) = a(b,c,d) + (a,c,d)b,$

$\displaystyle ({\text{ii)}}\;(a,a,a) = 0,$

$\displaystyle ({\text{iii)}}\;(a,b \circ c,d) = b \circ (a,c,d) + c \circ (a,b,d)$

for all $ a,b,c,d \in R$ and with $ x \circ y = (xy + yx)/2$. We prove that if $ R$ is semiprime, then $ R$ is alternative.

References [Enhancements On Off] (What's this?)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0393157-9
Keywords: Alternative, semiprime
Article copyright: © Copyright 1976 American Mathematical Society