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The lattice of subvarieties of the biregularization of the variety of Boolean algebras

Jerzy Płonka (2001)

Discussiones Mathematicae - General Algebra and Applications

Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by V b the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type τ b : + , · , ´ → N , where τ b ( + ) = τ b ( · ) = 2 and τ b ( ´ ) = 1 . In...

The lattice of varieties of fibered automata

Anna Mućka (2006)

Discussiones Mathematicae - General Algebra and Applications

The class of all fibered automata is a variety of two-sorted algebras. This paper provides a full description of the lattice of varieties of fibred automata.

The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz

J. Dudek (1996)

Colloquium Mathematicae

The main result of this paper is a description of totally commutative idempotent groupoids. In particular, we show that if an idempotent groupoid (G,·) has precisely m ≥ 2 distinct essentially binary polynomials and they are all commutative, then G contains a subgroupoid isomorphic to the groupoid N m described below. In [2], this fact was proved for m = 2.

The monoid of generalized hypersubstitutions of type τ = (n)

Wattapong Puninagool, Sorasak Leeratanavalee (2010)

Discussiones Mathematicae - General Algebra and Applications

A (usual) hypersubstitution of type τ is a function which takes each operation symbol of the type to a term of the type, of the same arity. The set of all hypersubstitutions of a fixed type τ forms a monoid under composition, and semigroup properties of this monoid have been studied by a number of authors. In particular, idempotent and regular elements, and the Green’s relations, have been studied for type (n) by S.L. Wismath. A generalized hypersubstitution of type τ=(n) is a mapping σ which takes...

The order of normalform hypersubstitutions of type (2)

Klaus Denecke, Kazem Mahdavi (2000)

Discussiones Mathematicae - General Algebra and Applications

In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].

The ordering of commutative terms

Jaroslav Ježek (2006)

Czechoslovak Mathematical Journal

By a commutative term we mean an element of the free commutative groupoid F of infinite rank. For two commutative terms a , b write a ≤ b if b contains a subterm that is a substitution instance of a . With respect to this relation, F is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered set has...

The positive and generalized discriminators don't exist

A.G. Pinus (2000)

Discussiones Mathematicae - General Algebra and Applications

In this paper it is proved that there does not exist a function for the language of positive and generalized conditional terms that behaves the same as the discriminator for the language of conditional terms.

Currently displaying 61 – 80 of 167