Algebraic atomistic lattices of quasivarieties

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

Research output: Contribution to journalReview article

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 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.

Original languageEnglish
Pages (from-to)213-225
Number of pages13
JournalAlgebra and Logic
Volume36
Issue number4
Publication statusPublished - Dec 1 1997

    Fingerprint

ASJC Scopus subject areas

  • Analysis
  • Logic

Cite this

Adaricheva, K. V., Gorbunov, V. A., & Dziobiak, W. (1997). Algebraic atomistic lattices of quasivarieties. Algebra and Logic, 36(4), 213-225.