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 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
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 journal › Article
}
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 -