### Abstract

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, ).

Original language | English |
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Article number | 1250066 |

Journal | International Journal of Algebra and Computation |

Volume | 22 |

Issue number | 7 |

DOIs | |

Publication status | Published - Nov 1 2012 |

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### Keywords

- Quasivariety
- congruence lattice
- representation
- semilattice

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*International Journal of Algebra and Computation*,

*22*(7), [1250066]. https://doi.org/10.1142/S021819671250066X