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On algebras satisfying the identity $ (yx)x+x(xy)=2(xy)x$


Author: Robert A. Chaffer
Journal: Proc. Amer. Math. Soc. 31 (1972), 376-380
DOI: https://doi.org/10.1090/S0002-9939-1972-0288153-2
MathSciNet review: 0288153
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Abstract | References | Additional Information

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

  • [1] A. A. Albert, Power-associative rings, Trans. Amer. Math. Soc. 64 (1948), 552-593. MR 10, 349. MR 0027750 (10:349g)
  • [2] F. Kosier, On a class of nonflexible algebras, Trans. Amer. Math. Soc. 102 (1962), 299-318. MR 24 #A3187. MR 0133353 (24:A3187)
  • [3] R. H. Oehmke, On flexible algebras, Ann. of Math. (2) 68 (1958), 221-230. MR 21 #5664. MR 0106934 (21:5664)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288153-2
Keywords: Noncommutative Jordan algebra, flexible algebra, strictly power-associative, degree of an algebra, stable algebra
Article copyright: © Copyright 1972 American Mathematical Society

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