Regularity of Linear Hypersubstitutions for Algebraic Systems of Type \(((n),(m))\) - Kumduang, Thodsaporn; Leeratanavalee, Sorasak (Communications in Mathematics and Applications, 2019)
An algebraic system consisting a nonempty set together with a sequence of operations and a sequence of relations on this set. The properties of this structure are expressed by terms and formulas. In this paper we study on linear terms of type \((n)\) for a natural number $n≥1$ and linear formulas of type \(((n),(m))\) for natural numbers \(n,m≥ 1\). Using the partial clone of linear terms and the partial clone of linear formulas, we define the new concept of linear hypersubstitutions for algebraic systems of type \(((n),(m))\) and proved that the set of all linear hypersubstitutions for algebraic systems of type \(((n),(m))\) with a binary operation on this set and the identity element forms a monoid. Finally, we also interest in studying the semigroup or monoid properties of its. In particular, we investigate the idempotency and regularity of linear hypersubstitutions for algebraic systems of this monoid.
Keywords: Algebraic systems; Linear terms; Linear formulas; Linear hypersubstitutions; Regular elements