Identities and Quasi-Identities of Pointed Algebras

Siberian Mathematical Journal - Each pointed enrichment of an algebra can be regarded as the same algebra with an additional finite set of constant operations. An algebra...     

On Locally Finite Modular Lattice Varieties of Finite Height

It is shown that the variety generated by a finite modular lattice has only finitely many locally finite covers.      

Finite lattices as relative congruence lattices of finite algebras

Let A be a finite algebra and a quasivariety. By A is meant the lattice of congruences θ on A with . For any positive integer n, we give conditions on a finite algebra A under which for any n-element lattice L there is a quasivariety such that . The author was supported by INTAS grant 03-51-4110.     

Finite Lattices as Lattices of Relative Congruences of Finite Unars and Abelian Groups

It is proved that every finite lattice is isomorphic to an R-congruence lattice of a finite unar (finite Abelian group), as well as to a lattice of R-varieties for some locally finite finitely axiomatizable quasivariety of unars (Abelian groups) R.     

A Semigroup of Theories and Its Lattice of Idempotent Elements

Algebra and Logic - On the set of all first-order theories T(σ) of similarity type σ, a binary operation {·} is defined by the rule T · S = Th({A × B | A |= T and B |= S})...     

Equational theories as congruences of enriched monoids

The problem of characterizing the lattices of equational theories is still unsolved. In this paper we describe a class of monoids enriched by two unary operations and show that a lattice L is a lattice of equational theories if and only if L is isomorphic to a lattice of congruences of some enriched monoid belonging to . The author was supported by INTAS grant 03-51-4110 and The Alexander von Humboldt Foundation.     

Structure of Quasivariety Lattices. IV. Nonstandard Quasivarieties

Siberian Mathematical Journal - In the previous articles of this series, some sufficient conditions were found for a quasivariety to possess continuum many subquasivarieties with certain...