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 -