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On the Partially Ordered Semigroup Generated by the Class Operators I,R,H,S,P

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Abstract

Let I, H, S, P be the usual class operators on universal algebras. For a class K of universal algebras of the same type, let R({K}) be the class of all algebras isomorphic to a retract of a member of K and let R denote the corresponding class operator. In this paper the semigroup generated by class operators I, R, H, S, P and the corresponding partially ordered set are described. Also the standard semigroups of the above operators are determined for some varieties.

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Authors and Affiliations

  1. Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Yugoslavia

    Rozália Sz. Madarász

  2. Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Boža Tasić

Authors
  1. Rozália Sz. Madarász
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  2. Boža Tasić
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Madarász, R.S., Tasić, B. On the Partially Ordered Semigroup Generated by the Class Operators I,R,H,S,P. Order 18, 49–60 (2001). https://doi.org/10.1023/A:1010614400132

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  • DOI: https://doi.org/10.1023/A:1010614400132

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