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On congruence distributivity of ordered algebras with constants

Krisztina Balog, Benedek Skublics (2011)

Discussiones Mathematicae - General Algebra and Applications

We define the order-congruence distributivity at 0 and order- congruence n-distributivity at 0 of ordered algebras with a nullary operation 0. These notions are generalizations of congruence distributivity and congruence n-distributivity. We prove that a class of ordered algebras with a nullary operation 0 closed under taking subalgebras and direct products is order-congruence distributive at 0 iff it is order-congruence n-distributive at 0. We also characterize such classes by a Mal'tsev condition....

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 distributive trices

Kiyomitsu Horiuchi, Andreja Tepavčević (2001)

Discussiones Mathematicae - General Algebra and Applications

A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.

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 free modes

Michał Marek Stronkowski (2006)

Commentationes Mathematicae Universitatis Carolinae

We prove a theorem describing the equational theory of all modes of a fixed type. We use this result to show that a free mode with at least one basic operation of arity at least three, over a set of cardinality at least two, does not satisfy identities selected by ’A. Szendrei in Identities satisfied by convex linear forms, Algebra Universalis 12 (1981), 103–122, that hold in any subreduct of a semimodule over a commutative semiring. This gives a negative answer to the question raised by A. Romanowska:...

On free Turing algebras

Herbert Lugowski (1986)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Currently displaying 21 – 40 of 114