Clones of Terms of a Fixed Variable

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