The semigroup of linear terms

Abstract

The set of linear terms, i.e. terms in which each variable occurs at most once, does not form a subsemigroup of the so-called diagonal semigroup. We consider the reduct of the diagonal semigroup to the linear terms, which is not a partial semigroup. We extend the set of linear terms by an expression “[Formula: see text]”, that is formally a linear term, obtaining a semigroup. The algebraic structure of this semigroup will be studied in this paper. We characterize the Green’s relations and the regular elements as well as the idempotent elements. Moreover, we discuss the ideal structure.