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Proceedings of the American Mathematical Society

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Algebras satisfying congruence relations


Authors: Raymond Coughlin, Michael Rich and Armin Thedy
Journal: Proc. Amer. Math. Soc. 51 (1975), 263-269
MSC: Primary 17AXX
DOI: https://doi.org/10.1090/S0002-9939-1975-0374200-9
MathSciNet review: 0374200
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Abstract: It is shown that the classical nonassociative algebras which have an identity element can be defined in terms of congruence relations modulo the base field.


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  • [1] T. Anderson, A note on derivations of commutative algebras, Proc. Amer. Math. Soc. 17 (1966), 1199-1202. MR 34 #4309. MR 0204469 (34:4309)
  • [2] R. Coughlin and M. Rich, Some associativity conditions for algebras, Amer. Math. Monthly 78 (1971), 1107. MR 45 #5176. MR 0296115 (45:5176)
  • [3] J. Goldman and S. Kass, Linearization in rings and algebras, Amer. Math. Monthly 76 (1969), 348-355. MR 39 # 2821. MR 0241481 (39:2821)
  • [4] E. Kleinfeld, Quasi-nil rings, Proc. Amer. Math. Soc. 10 (1959), 477-479. MR 21 # 3469. MR 0104716 (21:3469)
  • [5] J. M. Osborn, Varieties of algebras, Advances in Math. 8 (1972), 163-369. MR 44 #6775. MR 0289587 (44:6775)
  • [6] R. L. San Soucie, Right alternative division rings of characteristic two, Proc. Amer. Math. Soc. 6 (1955), 291-296. MR 16, 896; erratum 16, 1331. MR 0068526 (16:896e)
  • [7] R. D. Schafer, Noncommutative Jordan algebras of characteristic 0, Proc. Amer. Math. Soc. 6 (1955), 472-475. MR 17, 10. MR 0070627 (17:10c)
  • [8] -, An introduction to nonassociative algebras, Pure and Appl. Math., vol. 22, Academic Press, New York, 1966. MR 35 #1643. MR 0210757 (35:1643)
  • [9] A. Thedy, Right alternative rings, J. Algebra (to appear). MR 0384888 (52:5758)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0374200-9
Keywords: Alternative algebra, strongly alternative algebra, Jordan algebra, noncommutative Jordan algebra, flexible, Jordan-admissible
Article copyright: © Copyright 1975 American Mathematical Society

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