Partial Menger algebras of terms
- The superposition operation S-n,S-A, n >= 1, n is an element of N, maps to each (n + 1)-tuple of n-ary operations on a set A an n-ary operation on A and satisfies the so-called superassociative law, a generalization of the associative law. The corresponding algebraic structures are Menger algebras of rank n. A partial algebra of type (n + 1) which satisfies the superassociative law as weak identity is said to be a partial Menger algebra of rank n. As a generalization of linear terms we define r-terms as terms where each variable occurs at most r-times. It will be proved that n-ary r-terms form partial Menger algebras of rank n. 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 r-hypersubstitutions.U
Author details: | Klaus-Dieter DeneckeORCiDGND, Hippolyte HounnonGND |
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DOI: | https://doi.org/10.1142/S1793557121500923 |
ISSN: | 1793-5571 |
ISSN: | 1793-7183 |
Title of parent work (English): | Asian-European journal of mathematics |
Publisher: | World Scientific |
Place of publishing: | Singapore |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/06/01 |
Publication year: | 2021 |
Release date: | 2023/06/22 |
Tag: | Menger algebra of rank n; algebra of rank n; linear term; n-ary operation; n-ary term; partial Menger; r-hypersubstitution; r-term; superposition of n-ary operations and n-ary; terms |
Volume: | 14 |
Issue: | 06 |
Article number: | 2150092 |
Number of pages: | 14 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Bronze Open-Access |