Linear-Hypersubstitutions for Algebraic Systems of Type ((n); (n)) and Characterization of Their Idempotent Elements: Jintana Joomwong, Dara Phusanga
A formula in which each variable occurs at most once is said to be a linear-formula ([1, 2]). A linear-hypersubstitution for algebraic systems of type ((n);(n)) is a mapping σ__t,F which maps n-ary operation symbols f to n-ary linear-terms σ__t,F (f) and n-ary relational symbols γ to n-ary linear-formulas σ__t,F (γ). Any linear-hypersubstitution σ_t,F can be extended to a mapping σ__t,F on the set of all linear- terms of type (n) and linear-formulas of type ((n);(n)). A binary operation “°__lin ” on Hyp^lin((n);(n)) the set of all linear-hypersubstitutions for algebraic systems of type ((n);(n)) can be defined by using this extension. The set Hyp^lin((n);(n)) together with the identity linear-hypersubstitution (σ__t,F )__id which maps (σ__t,F )__id (f):=f(x_1,…,x_n) and (σ__t,F )__id (γ):=γ(x_1,…,x_n) forms a monoid. The concept of an idempotent element plays an important role in semigroup theory [3]. In this paper, we characterize the idempotent of the monoid of linear-hypersubstitutions for algebraic systems of type ((n);(n)). , journal=Thai Journal of Mathematics, author=Team, Support, year=2020, month=Jan., pages=93–102