A New Concept of Non-deterministic Hypersubstitutions for Algebraic Systems

The algebraic systems are well-established structures of classical universal algebras. An algebraic system is a triple consisting a nonempty set with the collection of operations and the collection of relations. The purpose of this paper, we extend the concepts related to non-deterministic hypersubstitutions (nd-hypersubstitutions) for universal algebras to algebraic systems and obtain that the set of all non-deterministic hypersubstitutions for algebraic systems forms a monoid with a binary operation defined on this set.