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Subquasivarieties of regularized varieties

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Abstract

This paper considers the lattice of subquasivarieties of a regular variety. In particular we show that if V is a strongly irregular variety that is minimal as a quasivariety, then the smallest quasivariety containing both V and SI (the variety of semilattices) is never equal to the regularization V of V.

We use this result to describe the lattice of subquasivarieties of V in several special but quite common, cases and give a number of applications and examples.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, 50011, Ames, IA, USA

    C. Bergman

  2. Institute of Mathematics, Warsaw Technical University, PL-00661, Plac Politechniki, Warsaw, Poland

    A. Romanowska

Authors
  1. C. Bergman
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  2. A. Romanowska
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Additional information

Work on this paper was begun while the second author was visiting Iowa State University during the summer of 1994.

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Bergman, C., Romanowska, A. Subquasivarieties of regularized varieties. Algebra Universalis 36, 536–563 (1996). https://doi.org/10.1007/BF01233924

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  • DOI: https://doi.org/10.1007/BF01233924

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