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Congruence computations in principal arithmetical varieties

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Abstract

This paper is a continuation of the earlier paper by the same authors in which a primary result was that every arithmetical affine complete variety of finite type is a principal arithmetical variety with respect to an appropriately chosen Pixley term. The paper begins by presenting an extension of this result to all finitely generated congruences and, as an example, constructs a closed form solution formula for any finitely presented system of pairwise compatible congruences (the Chinese remainder theorem). It is also shown that in all such varieties the meet of principal congruences is also principal, and finally, if a minimal generating algebra of the variety is regular, it is shown that the variety is also regular and the join of principal congruences is again principal.

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Authors and Affiliations

  1. University of Tartu, Tartu, Estonia

    Kalle Kaarli

  2. Harvey Mudd College, Claremont, California, 91711, USA

    Alden Pixley

Authors
  1. Kalle Kaarli
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  2. Alden Pixley
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Correspondence to Kalle Kaarli.

Additional information

Presented by E. Aichinger.

The research of Kalle Kaarli was partially supported by institutional research funding IUT20-57 of the Estonian Ministry of Education and Research. Work by both authors was supported by the Austrian Science Fund (FWF) P29931; Alden Pixley was a recipient of an Anthony B. Mirante Travel Grant.

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Kaarli, K., Pixley, A. Congruence computations in principal arithmetical varieties. Algebra Univers. 79, 88 (2018). https://doi.org/10.1007/s00012-018-0568-y

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  • DOI: https://doi.org/10.1007/s00012-018-0568-y

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