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Multi-hypersubstitutions and colored solid varieties

  • Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by operation symbols and by colors, i.e. certain positive integers. We are interested in mappings which map differently-colored operation symbols to different terms. In this paper we extend the theory of hypersubstitutions and solid varieties to multi-hypersubstitutions and colored solid varieties. We develop the interconnections between such colored terms and multihypersubstitutions and the equational theory of Universal Algebra. The collection of all varieties of a given type forms a complete lattice which is very complex and difficult to study; multi-hypersubstitutions and colored solid varieties offer a new method to study complete sublattices of this lattice.

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Metadaten
Author details:Klaus-Dieter DeneckeORCiDGND, Jörg KoppitzORCiDGND, Slavčo ŠtrakovGND
DOI:https://doi.org/10.1142/S0218196706003189
ISSN:0218-1967
Title of parent work (English):International journal of algebra and computation
Publisher:World Scient. Publ.
Place of publishing:Singapore
Publication type:Article
Language:English
Year of first publication:2006
Publication year:2006
Release date:2020/06/05
Tag:coloration of terms; colored solid varieties; multi-hypersubstitutions
Volume:16
Issue:4
Number of pages:19
First page:797
Last Page:815
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
Open Access / Green Open-Access
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