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- Title
LATTICES OF QUASI-EQUATIONAL THEORIES AS CONGRUENCE LATTICES OF SEMILATTICES WITH OPERATORS: PART I.
- Authors
ADARICHEVA, KIRA; NATION, J. B.
- Abstract
We show that for every quasivariety 풦 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 풦 (the dual of the lattice of sub-quasivarieties of 풦) is isomorphic to Con( S, +, 0, 풡. As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.
- Subjects
CONGRUENCE lattices; VARIETIES (Universal algebra); SEMILATTICES; OPERATOR theory; ISOMORPHISM (Mathematics); QUASIVARIETIES (Universal algebra)
- Publication
International Journal of Algebra & Computation, 2012, Vol 22, Issue 7, p-1
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196712500658