On generalizing alternative rings

Author:
D. J. Rodabaugh

Journal:
Proc. Amer. Math. Soc. **46** (1974), 157-163

MSC:
Primary 17D05

MathSciNet review:
0349786

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Abstract: Consider a ring that satisfies the identity and any two of the three identities: . In this paper, we prove that if has characteristic prime to 6 then semiprime with idempotent implies has a Peirce decomposition in which the modules multiply as they do in an alternative ring. If in addition is prime with idempotent then is alternative.

**[1]**Seyoum Getu and D. J. Rodabaugh,*Generalizing alternative rings*, Comm. Algebra**2**(1974), 35–81. MR**0352195****[2]**Erwin Kleinfeld,*Generalization of alternative rings. I, II*, J. Algebra 18 (1971), 304-325; ibid.**18**(1971), 326–339. MR**0274545****[3]**Harry F. Smith,*Prime generalized alternative rings 𝐼 with nontrivial idempotent*, Proc. Amer. Math. Soc.**39**(1973), 242–246. MR**0313348**, 10.1090/S0002-9939-1973-0313348-X

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0349786-X

Keywords:
Alternative ring,
prime ring,
semiprime ring

Article copyright:
© Copyright 1974
American Mathematical Society