Clones of Terms of a Fixed Variable

Khwancheewa Wattanatripop and Thawhat Changphas
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Khwancheewa Wattanatripop: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Thawhat Changphas: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Mathematics, 2020, vol. 8, issue 2, 1-9

Abstract: Let τ be a type of algebras. This paper introduces special terms of type τ called terms of a fixed variable. It turns out that the set of all terms of a fixed variable of type τ forms the many-sorted clone satisfying the superassociative law as identity, under the many-sorted superposition operations. Moreover, based on terms of a fixed variable of type τ , hypersubstitutions of a fixed variable and the related closed identities of a fixed variable and closed variety of a fixed variable are introduced and studied.

Keywords: clone; term; terms of a fixed variable; hypersubstitutions of a fixed variable; closed identities of a fixed variable; closed variety of a fixed variable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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