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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 classification of rational languages by semilattice-ordered monoids

Libor Polák (2004)

Archivum Mathematicum

We prove here an Eilenberg type theorem: the so-called conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilattice-ordered monoids. Taking complements of members of a conjunctive variety of languages we get a so-called disjunctive variety. We present here a non-trivial example of such a variety together with an equational characterization of the corresponding pseudovariety.

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