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Homomorphisms of unary algebras with a given quotient

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Abstract

For a unary algebraA withκ≥2 fundamental operations, letH(A) denote the class of all unary algebras that have a homomorphisrn intoA, and let the classQ(A) consist of all algebras havingA as one of their quotients. IfA is freely indecomposable then H(A) andQ(A) are shown to be categorically universal if and only if either class contains a rigid algebra; this, in turn, is equivalent to the absence of homomorphisms fromA into a free algebra.

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Authors and Affiliations

  1. State University of New York, 12561, New Paltz, New York, USA

    M. E. Adams & J. Sichler

  2. University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    M. E. Adams & J. Sichler

Authors
  1. M. E. Adams
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  2. J. Sichler
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The support of the NSERC is gratefully acknowledged.

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Adams, M.E., Sichler, J. Homomorphisms of unary algebras with a given quotient. Algebra Universalis 27, 194–219 (1990). https://doi.org/10.1007/BF01182453

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  • DOI: https://doi.org/10.1007/BF01182453

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