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The Set of Quasi-Identities of an Algebra

  • A. A. Klein

Abstract

Let F = k{X} be the free associative algebra over a field k, X an infinite countable set. It is well-known that the set of polynomial identities I(R) of a given k-algebra R is a T-ideal, namely an ideal of F which is invariant under all the algebra endomorphisms of F. Moreover, if J is a T-ideal then J = I(F/ J) [3, p. 61].

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References

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    Cohn, P. M. Universal Algebra (2nd ed.), D. Reidel, Dordrecht, 1981.zbMATHCrossRefGoogle Scholar
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    Cohn, P. M. Free rings and their relations (2nd ed.) Acad. Press, 1985.Google Scholar
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    Jacobson, N. Pi-algebras, Lect. Notes in Math. 441, Springer-Verlag, 1975.Google Scholar
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    Klein, A. A. Necessary conditions for embedding rings into fields, Trans. Amer. Math. Soc. 137 (1969), 141–151.MathSciNetzbMATHCrossRefGoogle Scholar
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    Mal’cev, A. I. Algebraic Systems, Springer-Verlag, 1973.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • A. A. Klein
    • 1
  1. 1.Raymond and Beverly Sackler, Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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