The Clone of K*(n, r)-Full Terms

Discussiones Mathematicae - General Algebra and Applications

Wattanatripop Khwancheewa¹  Changphas Thawhat¹ 

[1] Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand;

关键词: restricted range transformation;    full term;    clone;    menger algebra;    hypersubstitution;    hyperidentity;    solid variety;    08b15;    08a62;    08b05;   

DOI  :  10.7151/dmgaa.1319

来源: DOAJ

【 摘 要 】

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].

【 授权许可】

Unknown