### Abstract

The Gorbunov-Tumanov conjecture on the structure of lattices of quasivarieties is proved true for the case of algebraic lattices. Namely, for an algebraic atomistic lattice L, the following conditions are equivalent: (1) L is represented as L_{q}(K) for some algebraic quasivariety K; (2) L is represented as S∧(A) for some algebraic lattice A which satisfies the minimality condition and nearly satisfies the maximality condition; (3) L is a coalgebraic lattice admitting an equaclosure operator.

Original language | English |
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Pages (from-to) | 213-225 |

Number of pages | 13 |

Journal | Algebra and Logic |

Volume | 36 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1997 |

### ASJC Scopus subject areas

- Analysis
- Logic

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## Cite this

Adaricheva, K. V., Gorbunov, V. A., & Dziobiak, W. (1997). Algebraic atomistic lattices of quasivarieties.

*Algebra and Logic*,*36*(4), 213-225. https://doi.org/10.1007/s10469-997-0063-6