Idempotence and Regularity of Generlized Relational Hypersubstitutions for Algebraic Sytems
Pornpimol Kunama, Sorasak Leeratanavalee · Discussiones Mathematicae - General Algebra and Applications · 2024
The concept of a generalized relational hypersubstitution for algebraic systems of type (τ, τ ′ ) is an extension of the concept of a generalized hypersubstitutions for universal algebra of type τ .The set of all generalized relational hypersubstitutions for algebraic systems of type (τ, τ ′ ) together with a binary operation defined on the set and its identity forms a monoid.The properties of this structure are expressed by terms and relational terms.In this paper, we study the semigroup properties of the monoid of type ((n), (m)) for arbitrary natural numbers n, m ≥ 2. In particular, we characterize the idempotent as well as regular elements in this submonoid.