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On nondistributive Steiner quasigroups

A. Marczak (1997)

Colloquium Mathematicae

A well known result of R. Dedekind states that a lattice is nonmodular if and only if it has a sublattice isomorphic to N 5 . Similarly a lattice is nondistributive if and only if it has a sublattice isomorphic to N 5 or M 3 (see [11]). Recently a few results in this spirit were obtained involving the number of polynomials of an algebra (see e.g. [1], [3], [5], [6]). In this paper we prove that a nondistributive Steiner quasigroup (G,·) has at least 21 essentially ternary polynomials (which improves the...

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 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.

On reductive and distributive algebras

Anna B. Romanowska (1999)

Commentationes Mathematicae Universitatis Carolinae

The paper investigates idempotent, reductive, and distributive groupoids, and more generally Ω -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left k -step reductive Ω -algebras, and of right n -step reductive Ω -algebras, are independent for any positive integers k and n . This gives a structural description of algebras in the join of...

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.

On some congruences of power algebras

Agata Pilitowska, Anna Zamojska-Dzienio (2012)

Open Mathematics

In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. In this paper we investigate extended power algebras (power algebras of non-empty subsets with one additional semilattice operation) of modes (entropic and idempotent algebras). We describe some congruence relations on these algebras such that their quotients are idempotent. Such congruences determine some class...

On some constructions of algebraic objects

Miroslav Novotný (2006)

Czechoslovak Mathematical Journal

Mono-unary algebras may be used to construct homomorphisms, subalgebras, and direct products of algebras of an arbitrary type.

Currently displaying 361 – 380 of 891