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( L , ϕ ) -representations of algebras

Andrzej Walendziak (1993)

Archivum Mathematicum

In this paper we introduce the concept of an ( L , ϕ ) -representation of an algebra A which is a common generalization of subdirect, full subdirect and weak direct representation of A . Here we characterize such representations in terms of congruence relations.

2-normalization of lattices

Ivan Chajda, W. Cheng, S. L. Wismath (2008)

Czechoslovak Mathematical Journal

Let τ be a type of algebras. A valuation of terms of type τ is a function v assigning to each term t of type τ a value v ( t ) ≥ 0 . For k ≥ 1 , an identity s ≈ t of type τ is said to be k -normal (with respect to valuation v ) if either s = t or both s and t have value ≥ k . Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called k -normal (with respect to the valuation v ) if all its identities are k -normal. For any variety V , there is a least...

A duality between infinitary varieties and algebraic theories

Jiří Adámek, Václav Koubek, Jiří Velebil (2000)

Commentationes Mathematicae Universitatis Carolinae

A duality between λ -ary varieties and λ -ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal λ , whenever λ -small products commute with 𝒟 -colimits in Set , then 𝒟 must be a λ -filtered category. We nevertheless introduce the concept of λ -sifted colimits so that morphisms between λ -ary varieties (defined to be λ -ary, regular right adjoints) are precisely the functors...

A duality for isotropic median algebras

Miroslav Ploščica (1992)

Commentationes Mathematicae Universitatis Carolinae

We establish categorical dualities between varieties of isotropic median algebras and suitable categories of operational and relational topological structures. We follow a general duality theory of B.A. Davey and H. Werner. The duality results are used to describe free isotropic median algebras. If the number of free generators is less than five, the description is detailed.

A Finite Axiomatization of Nondeterministic Regular Expressions

Flavio Corradini, Rocco De Nicola, Anna Labella (2010)

RAIRO - Theoretical Informatics and Applications

An alternative (tree-based) semantics for a class of regular expressions is proposed that assigns a central rôle to the + operator and thus to nondeterminism and nondeterministic choice. For the new semantics a consistent and complete axiomatization is obtained from the original axiomatization of regular expressions by Salomaa and by Kozen by dropping the idempotence law for + and the distribution law of • over +.

A multiplication of e -varieties of orthodox semigroups

Martin Kuřil (1995)

Archivum Mathematicum

We define semantically a partial multiplication on the lattice of all e–varieties of regular semigroups. In the case that the first factor is an e–variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences.

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