Algebraic atomistic lattices of quasivarieties

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

Research output: Contribution to journalArticle

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 - 1997
Externally publishedYes

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Quasivariety
Algebraic Lattice
Minimality
Operator

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.

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

In: Algebra and Logic, Vol. 36, No. 4, 1997, p. 213-225.

Research output: Contribution to journalArticle

Adaricheva, KV, Gorbunov, VA & Dziobiak, W 1997, 'Algebraic atomistic lattices of quasivarieties', Algebra and Logic, vol. 36, no. 4, pp. 213-225.
Adaricheva KV, Gorbunov VA, Dziobiak W. Algebraic atomistic lattices of quasivarieties. Algebra and Logic. 1997;36(4):213-225.
Adaricheva, K. V. ; Gorbunov, V. A. ; Dziobiak, W. / Algebraic atomistic lattices of quasivarieties. In: Algebra and Logic. 1997 ; Vol. 36, No. 4. pp. 213-225.
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