A note on generalizing alternative rings
HTML articles powered by AMS MathViewer
- by Irvin Roy Hentzel and Giulia Maria Piacentini Cattaneo PDF
- Proc. Amer. Math. Soc. 55 (1976), 6-8 Request permission
Abstract:
Let $R$ be a nonassociative ring of characteristic different from $2$ and $3$ which satisfies the following identities: \[ ({\text {i)}}\;(ab,c,d) + (a,b,[c,d]) = a(b,c,d) + (a,c,d)b,\] \[ ({\text {ii)}}\;(a,a,a) = 0,\] \[ ({\text {iii)}}\;(a,b \circ c,d) = b \circ (a,c,d) + c \circ (a,b,d)\] 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
- Seyoum Getu and D. J. Rodabaugh, Generalizing alternative rings, Comm. Algebra 2 (1974), 35–81. MR 352195, DOI 10.1080/00927877408822004
- Irvin Roy Hentzel and Giulia Maria Piacentini Cattaneo, Semi-prime generalized right alternative rings, J. Algebra 43 (1976), no. 1, 14–27. MR 422374, DOI 10.1016/0021-8693(76)90140-X
- Erwin Kleinfeld, Right alternative rings, Proc. Amer. Math. Soc. 4 (1953), 939–944. MR 59888, DOI 10.1090/S0002-9939-1953-0059888-X
- D. J. Rodabaugh, On generalizing alternative rings, Proc. Amer. Math. Soc. 46 (1974), 157–163. MR 349786, DOI 10.1090/S0002-9939-1974-0349786-X
- Armin Thedy, Right alternative rings, J. Algebra 37 (1975), no. 1, 1–43. MR 384888, DOI 10.1016/0021-8693(75)90086-1
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 6-8
- DOI: https://doi.org/10.1090/S0002-9939-1976-0393157-9
- MathSciNet review: 0393157