### 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 |
---|---|

Pages (from-to) | 213-225 |

Number of pages | 13 |

Journal | Algebra and Logic |

Volume | 36 |

Issue number | 4 |

Publication status | Published - 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis
- Logic

### Cite this

*Algebra and Logic*,

*36*(4), 213-225.

**Algebraic atomistic lattices of quasivarieties.** / Adaricheva, K. V.; Gorbunov, V. A.; Dziobiak, W.

Research output: Contribution to journal › Article

*Algebra and Logic*, vol. 36, no. 4, pp. 213-225.

}

TY - JOUR

T1 - Algebraic atomistic lattices of quasivarieties

AU - Adaricheva, K. V.

AU - Gorbunov, V. A.

AU - Dziobiak, W.

PY - 1997

Y1 - 1997

N2 - 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 Lq(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.

AB - 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 Lq(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.

UR - http://www.scopus.com/inward/record.url?scp=27544514670&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27544514670&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:27544514670

VL - 36

SP - 213

EP - 225

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 4

ER -