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Algebra universalis

, 79:88 | Cite as

Congruence computations in principal arithmetical varieties

  • Kalle Kaarli
  • Alden Pixley
Article
  • 11 Downloads

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.

Keywords

Principal arithmetical varieties Affine complete varieties Congruence computations Chinese remainder theorem Discriminator 

Mathematics Subject Classification

08A30 08A40 08B05 08B10 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of TartuTartuEstonia
  2. 2.Harvey Mudd CollegeClaremontUSA

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