Algebraic atomistic lattices of quasivarieties

K. V. Adaricheva; V. A. Gorbunov; W. Dziobiak

doi:10.1007/s10469-997-0063-6

Algebraic atomistic lattices of quasivarieties

K. V. Adaricheva, V. A. Gorbunov, W. Dziobiak

Department of Mathematics

Research output: Contribution to journal › Review article › peer-review

10 Citations (Scopus)

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
DOIs	https://doi.org/10.1007/s10469-997-0063-6
Publication status	Published - Jan 1 1997

ASJC Scopus subject areas

Analysis
Logic

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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.

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