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Algebra universalis

, 79:78 | Cite as

Congruences on near-Heyting algebras

  • Luciano J. González
  • Marina B. Lattanzi
Article
  • 33 Downloads

Abstract

A near-Heyting algebra is a join-semilattice with a top element such that every principal upset is a Heyting algebra. We establish a one-to-one correspondence between the lattices of filters and congruences of a near-Heyting algebra. To attain this aim, we first show an embedding from the lattice of filters to the lattice of congruences of a distributive nearlattice. Then, we describe the subdirectly irreducible and simple near-Heyting algebras. Finally, we fully characterize the principal congruences of distributive nearlattices and near-Heyting algebras. We conclude that the varieties of distributive nearlattices and near-Heyting algebras have equationally definable principal congruences.

Keywords

Near-Heyting algebra Distributive nearlattice Congruences Principal congruences 

Mathematics Subject Classification

06A12 06B10 08B26 06D20 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y NaturalesSanta RosaArgentina

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