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On covariety lattices

Tomasz Brengos (2008)

Discussiones Mathematicae - General Algebra and Applications

This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice L C V ( K ) 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 P κ -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 Equational Theory of Left Divisible Left Distributive Groupoids

Přemysl Jedlička (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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 a a 2 surjective lies in the variety generated by the left distributive left quasigroups.

On Jónsson's theorem

Diego Vaggione (1996)

Mathematica Bohemica

A proof of Jonsson's theorem inspired by considering a natural topology on algebraic lattices is given.

On modular elements of the lattice of semigroup varieties

Boris M. Vernikov (2007)

Commentationes Mathematicae Universitatis Carolinae

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 u = v is called substitutive if the words u and v depend on the same letters and v may be obtained from u by renaming of letters.) We completely determine all commutative modular...

On quasivarieties of nilpotent Moufang loops. II

Vasile I. Ursu (2012)

Commentationes Mathematicae Universitatis Carolinae

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.

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