On algebras satisfying the identity $(yx)x+x(xy)=2(xy)x$
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- by Robert A. Chaffer PDF
- Proc. Amer. Math. Soc. 31 (1972), 376-380 Request permission
Abstract:
Simple, strictly power-associative algebras satisfying the identity $(yx)x + x(xy) = 2(xy)x$ over a field of characteristic not 2 or 3 have been classified by F. Kosier as commutative Jordan, quasi-associative, or of degree less than three. In the present paper those of degree three or greater are shown to be commutative, which eliminates the quasi-associative case mentioned above.References
- A. A. Albert, Power-associative rings, Trans. Amer. Math. Soc. 64 (1948), 552–593. MR 27750, DOI 10.1090/S0002-9947-1948-0027750-7
- Frank Kosier, On a class of nonflexible algebras, Trans. Amer. Math. Soc. 102 (1962), 299–318. MR 133353, DOI 10.1090/S0002-9947-1962-0133353-3
- Robert H. Oehmke, On flexible algebras, Ann. of Math. (2) 68 (1958), 221–230. MR 106934, DOI 10.2307/1970244
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 376-380
- DOI: https://doi.org/10.1090/S0002-9939-1972-0288153-2
- MathSciNet review: 0288153