SOME TYPES OF PARTIAL GENERALIZED HYPERSUBTITUTIONS OF MANY-SORTED ALGEBRAS
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 . In 2000, S. Leeratanavalee and K. Denecke  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  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.