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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 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 permutability in semigroup varieties

Bedřich Pondělíček (1991)

Mathematica Bohemica

The paper contains characterizations of semigroup varieties whose semigroups with one generator (two generators) are permutable. Here all varieties of regular * -semigroups are described in which each semigroup with two generators is permutable.

On schemes for congruence distributivity

I. Chajda, R. Halaš (2004)

Open Mathematics

We present diagrammatic schemes characterizing congruence 3-permutable and distributive algebras. We show that a congruence 3-permutable algebra is congruence meetsemidistributive if and only if it is distributive. We characterize varieties of algebras satisfying the so-called triangular scheme by means of a Maltsev-type condition.

Orthorings

Ivan Chajda, Helmut Länger (2004)

Discussiones Mathematicae - General Algebra and Applications

Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.

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