Minimal varieties of -groups.
Modular median algebras generated by some partial modular median algebras
M-Solid Subvarieties of some Varieties of Commutative Semigroups
∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.The basic concepts are M -hyperidentities, where M is a monoid of hypersubstitutions. The set of all M -solid varieties of semigroups forms a complete sublattice of the lattice of all varieties of semigroups. We fix some specific varieties V of commutative semigroups and study the set of all M -solid subvarieties of V , in particular, if V is nilpotent.
On a multiplication of semigroup varieties.
On a simple one-element extension of left zero semigroups
On algebras and clones.
On automorphisms of the lattice of quasivarieties of lattice-ordered groups
On basic and axiomatic ranks of nilpotent varieties of Lie algebras
On convexities of lattices
On covariety lattices
This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a -coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras, such that...
On covers in the lattice of representable -varieties
On cross semigroup varieties and related questions.
On Equational Classes of Algebraic Versions of Logic I.
On Equational Theory of Left Divisible Left Distributive Groupoids
It is an open question whether the variety generated by the left divisible left distributive groupoids coincides with the variety generated by the left distributive left quasigroups. In this paper we prove that every left divisible left distributive groupoid with the mapping surjective lies in the variety generated by the left distributive left quasigroups.
On Jónsson's theorem
A proof of Jonsson's theorem inspired by considering a natural topology on algebraic lattices is given.
On lattices of varieties of universal algebras
On modular elements of the lattice of semigroup varieties
A semigroup variety is called modular if it is a modular element of the lattice of all semigroup varieties. We obtain a strong necessary condition for a semigroup variety to be modular. In particular, we prove that every modular nil-variety may be given by 0-reduced identities and substitutive identities only. (An identity is called substitutive if the words and depend on the same letters and may be obtained from by renaming of letters.) We completely determine all commutative modular...
On quasivarieties of nilpotent Moufang loops. I
In this part the smallest non-abelian quasivarieties for nilpotent Moufang loops are described.
On quasivarieties of nilpotent Moufang loops. II
In this part of the paper we study the quasiidentities of the nilpotent Moufang loops. In particular, we solve the problem of finite basis for quasiidentities in the finitely generated nilpotent Moufang loop.
On quasivarieties of partial algebras, their generation and their subquasivarieties. I