Algebraic atomistic lattices of quasivarieties

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_Λ (A) for some algebraic lattice A which satisfies the minimality condition and nearly satisfies the maximality conditions; (3) L is a coalgebraic lattice admitting an equaclosure operator. Supported by RFFR grants Nos. 96-01-01525 and 96-0-000976, and by DFG grant No. 436 (RUS) 113/2670. Translated from Algebra i Logika, Vol. 36, No. 4, pp. 363–386, July–August, 1997.