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The Clone of K*(n, r)-Full Terms.
- Source :
-
Discussiones Mathematicae: General Algebra & Applications . Dec2019, Vol. 39 Issue 2, p277-288. 12p. - Publication Year :
- 2019
-
Abstract
- Let τn be a type of algebras in which all operation symbols have arity n, for a fixed n ≥ 1. For 0 < r ≤ n, this paper introduces a special kind of n-ary terms of type τn called K*(n, r)-full terms. The set of all K*(n, r)-full terms of type τn is closed under the superposition operation Sn; hence forms a clone denoted by cloneK*(n,r)(τn). We prove that cloneK* (n,r)(τn) is a Menger algebra of rank n. We study K*(n, r)-full hypersubstitutions and the related K*(n, r)-full closed identities and K*(n, r)-full closed varieties. A connection between identities in cloneK* (n,r)(τn) and K* (n, r)-full closed identities is established. The results obtained generalize the results of Denecke and Jampachon [K. Denecke and P. Jampachon, Clones of full terms, Algebra and Discrete Math. 4 (2004) 1–11]. [ABSTRACT FROM AUTHOR]
- Subjects :
- *TERMS & phrases
*ALGEBRA
*SIGNS & symbols
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 15099415
- Volume :
- 39
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Discussiones Mathematicae: General Algebra & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 139631484
- Full Text :
- https://doi.org/10.7151/dmgaa.1319