Right regular and left regular elements of E-order-preserving transformation semigroups
Chaiwat Namnak, Ekkachai Laysirikul · International Journal of Algebra · 2013
Let (X, ≤) be a totally ordered set, E an arbitrary equivalence on X and T(X) the full transformation semigroup on X. We consider a subsemigroup of T(X) defined by EOP(X )= {α ∈ T(X ):( a, b) ∈ E and a ≤ b ⇒ (aα, bα) ∈ E and aα ≤ bα} which is called the E-order-preserving transformation semigroup on X. The purpose of this paper is to characterize when elements of EOP(X) are regular, left regular and right regular.