TY - JOUR

T1 - Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part II

AU - Adaricheva, Kira

AU - Nation, J. B.

N1 - Funding Information:
The authors were supported in part by a grant from the U.S. Civilian Research and Development Foundation. The first author was also supported in part by INTAS Grant N03-51-4110.

PY - 2012/11

Y1 - 2012/11

N2 - Part I proved that for every quasivariety of structures (which may have both operations and relations) there is a semilattice S with operators such that the lattice of quasi-equational theories of (the dual of the lattice of sub-quasivarieties of ) is isomorphic to Con(S, +, 0, ). It is known that if S is a join semilattice with 0 (and no operators), then there is a quasivariety such that the lattice of theories of is isomorphic to Con(S, +, 0). We prove that if S is a semilattice having both 0 and 1 with a group of operators acting on S, and each operator in fixes both 0 and 1, then there is a quasivariety such that the lattice of theories of is isomorphic to Con(S, +, 0, ).

AB - Part I proved that for every quasivariety of structures (which may have both operations and relations) there is a semilattice S with operators such that the lattice of quasi-equational theories of (the dual of the lattice of sub-quasivarieties of ) is isomorphic to Con(S, +, 0, ). It is known that if S is a join semilattice with 0 (and no operators), then there is a quasivariety such that the lattice of theories of is isomorphic to Con(S, +, 0). We prove that if S is a semilattice having both 0 and 1 with a group of operators acting on S, and each operator in fixes both 0 and 1, then there is a quasivariety such that the lattice of theories of is isomorphic to Con(S, +, 0, ).

KW - Quasivariety

KW - congruence lattice

KW - representation

KW - semilattice

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U2 - 10.1142/S021819671250066X

DO - 10.1142/S021819671250066X

M3 - Article

AN - SCOPUS:84870619878

VL - 22

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 7

M1 - 1250066

ER -