Monoid of linear hypersubstitutions for algebraic systems of type ((n), (2)) and its regularity

Abstract

© 2019, Prince of Songkla University. All rights reserved. An algebraic system is a structure which consists of a nonempty set together with a sequence of operations and a sequence of relations on this set. Properties of this structure are expressed in terms and formulas. In this paper, we show that the set of all linear hypersubstitutions for algebraic systems of the type ((n), (2)) with a binary operation on this set and the identity element forms a monoid. Finally, we characterize idempotent and regular elements on the monoid.