LATTICES OF QUASI-EQUATIONAL THEORIES AS CONGRUENCE LATTICES OF SEMILATTICES WITH OPERATORS: PART I-Reference-Cited by-同舟云学术

LATTICES OF QUASI-EQUATIONAL THEORIES AS CONGRUENCE LATTICES OF SEMILATTICES WITH OPERATORS: PART I

Published:2012-11 Issue:07 Volume:22 Page:1250065
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

ADARICHEVA KIRA¹,NATION J. B.²

Affiliation:

1. Department of Mathematical Sciences, Yeshiva University, New York, NY 10016, USA

2. Department of Mathematics, University of Hawaii, Honolulu, HI 96822, USA

Abstract

We show that for every quasivariety 𝒦 of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of 𝒦 (the dual of the lattice of sub-quasivarieties of 𝒦) is isomorphic to Con(S, +, 0, 𝒡. As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196712500658

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