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Operators and products in the lattice of existence

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A Corrigendum to this article was published on 01 December 1996

Abstract

The authors recently [34] established the existence of seven complete congruences {K, T, T l ,T r ,K t ,K r ,M} on the lattice\(\mathcal{L}_{ev} (\mathcal{R}\mathcal{S})\) of existence varieties of regular semigroups. For each such congruence ρ and each\(\mathcal{U} \in \mathcal{L}_{ev} (\mathcal{R}\mathcal{S})\), the ρ-class of\(\mathcal{U}\) is an interval\(\left[ {\mathcal{U}_\rho ,\mathcal{U}^\rho } \right]\) and it was previously established that thee-varieties of the form\(\mathcal{U}^\rho \) are Mal'cev products with\(\mathcal{U}\) of simplee-varieties such as rectangular bands, groups, left groups, etc. The principal objective of this paper is to employ semidirect products and wreath products to derive alternative descriptions of four of thee-varieties of the form\(\mathcal{U}^\rho \).

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Authors and Affiliations

  1. Department of Mathematics & Statistics, Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    Norman R. Reilly & Shuhua Zhang

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  1. Norman R. Reilly
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  2. Shuhua Zhang
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Additional information

Communicated by F. Pastijn

This work was supported, in part, by NSERC Grant 4044.

An erratum to this article is available at http://dx.doi.org/10.1007/BF02574142.

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Reilly, N.R., Zhang, S. Operators and products in the lattice of existence. Semigroup Forum 53, 1–24 (1996). https://doi.org/10.1007/BF02574117

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