SOME TYPES OF PARTIAL GENERALIZED HYPERSUBTITUTIONS OF MANY-SORTED ALGEBRAS

Abstract

One of important study in Universal algebra is to classify algebras into varieties and classify varieties into hypervarieties. The concept of a hypersubstitution, which is a tool used to study hyperidentities, was introduced by K. Denecke, D. Lau, R. P¨oschel and D. Schweigert [3]. In 2000, S. Leeratanavalee and K. Denecke [6] extended the above concept to the concept of a generalized hypersubstitution. In Universal algebra, we do not study only algebras which have one base set but many base sets. In 1970, G. Birkhoff and John D. Lipson [1] extended the concept of base structure of algebras from one-sorted to many-sorted, that is called heterogeneous algebras or many-sorted algebras. In this present paper, we show that the set of partial generalized hypersubstitutions Σ|I|,n(i)- HypG forms a monoid.