Alternators of a right alternative algebra

Author:
Irvin Roy Hentzel

Journal:
Trans. Amer. Math. Soc. **242** (1978), 141-156

MSC:
Primary 17A30

MathSciNet review:
496800

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Abstract: We show that in any right alternative algebra, the additive span of the alternators is nearly an ideal. We give an easy test to use to determine if a given set of additional identities will imply that the span of the alternators is an ideal. We apply our technique to the class of right alternative algebras satisfying the condition . We show that any semiprime algebra over a field of characteristic , which satisfies the right alternative law and the above identity with is a subdirect sum of (associative and commutative) integral domains.

**[1]**Larry Dornhoff,*Group representation theory. Part A: Ordinary representation theory*, Marcel Dekker, Inc., New York, 1971. Pure and Applied Mathematics, 7. MR**0347959****[2]**Irvin Roy Hentzel,*Processing identities by group representation*, Computers in nonassociative rings and algebras (Special session, 82nd Annual Meeting Amer. Math. Soc., San Antonio, Tex., 1976) Academic Press, New York, 1977, pp. 13–40. MR**0463251****[3]**Irvin Roy Hentzel, Giulia Maria Piacentini Cattaneo, and Denis Floyd,*Alternator and associator ideal algebras*, Trans. Amer. Math. Soc.**229**(1977), 87–109. MR**0447361**, 10.1090/S0002-9947-1977-0447361-7**[4]**N. McCoy,*Rings and ideals*, The Carus Mathematical Monographs, No. 8, Math. Assoc. of America.**[5]**Armin Thedy,*Right alternative rings*, J. Algebra**37**(1975), no. 1, 1–43. MR**0384888**

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0496800-5

Keywords:
Right alternative,
alternator ideal

Article copyright:
© Copyright 1978
American Mathematical Society