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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Polynomial identities of incidence algebras


Author: Robert B. Feinberg
Journal: Proc. Amer. Math. Soc. 55 (1976), 25-28
MSC: Primary 16A38
DOI: https://doi.org/10.1090/S0002-9939-1976-0404321-4
MathSciNet review: 0404321
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Abstract: In this paper we determine the polynomial identities satisfied by incidence algebras. One of our results is logically equivalent to the Amitsur-Levitzki Theorem on the polynomial identities satisfied by $ {K_n}$, the algebra of of $ n \times n$ matrices over a field $ K$.


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

  • [1] Peter Doubilet, Gian-Carlo Rota, and Richard Stanley, On the foundations of combinatorial theory. VI. The idea of generating function, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 267–318. MR 0403987
  • [2] R. B. Feinberg, Characterization of incidence algebras, (in preparation).
  • [3] Donald S. Passman, Infinite group rings, Marcel Dekker, Inc., New York, 1971. Pure and Applied Mathematics, 6. MR 0314951

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0404321-4
Keywords: Chain, incidence algebra, polynomial identity, quasi-ordered set
Article copyright: © Copyright 1976 American Mathematical Society