Partial Menger algebras of terms

Author:

Denecke K.1,Hounnon H.2

Affiliation:

1. Institute of Mathematics, University of Potsdam, Potsdam, Germany

2. Department of Mathematics, University of Abomey-Calavi, Benin

Abstract

The superposition operation [Formula: see text] [Formula: see text] [Formula: see text], maps to each [Formula: see text]-tuple of [Formula: see text]-ary operations on a set [Formula: see text] an [Formula: see text]-ary operation on [Formula: see text] and satisfies the so-called superassociative law, a generalization of the associative law. The corresponding algebraic structures are Menger algebras of rank [Formula: see text]. A partial algebra of type [Formula: see text] which satisfies the superassociative law as weak identity is said to be a partial Menger algebra of rank [Formula: see text]. As a generalization of linear terms we define [Formula: see text]-terms as terms where each variable occurs at most [Formula: see text]-times. It will be proved that [Formula: see text]-ary [Formula: see text]-terms form partial Menger algebras of rank [Formula: see text]. In this paper, some algebraic properties of partial Menger algebras such as generating systems, homomorphic images and freeness are investigated. As generalization of hypersubstitutions and linear hypersubstitutions we consider [Formula: see text]-hypersubstitutions.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

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