On certain semigroups of full contractions of a finite chain

Abstract

Let [n] = {1, 2, . . . , n} be a finite chain and let Tn be the semigroup of full transformations on [n].In this paper, we give a necessary and sufficient condition for an element to be regular and characterize all the Green's equivalences for the semigroup CT n. We further show that the semigroup CT n is left abundant semigroup.

On certain Semigroup of Order-decreasing Full Contraction Mappings of a Finite Chain

“…Partial order relations on various semigroups of the partial transformations have been investigated by many authors, see for example [6,18,21,20]. It is worth noting that the semigroup OCT n is not regular (see [32]). In this section, we characterize the partial order relation defined above on the semigroups OCT n and ODCT n , respectively.…”

On certain semigroups of contraction mappings of a finite chain

“…Moreover, ⟨A⟩ = A if and only if A is a subsemigroup of S and if ⟨A⟩ = S then A is said to generate S. Recall from section one that an element α ∈ CT n is an idempotent if and only if x i ∈ A i for 1 ⩽ i ⩽ p, that is to say the blocks A i are stationary [21]. We begin by recalling the following known characterization of regular elements in CT n from [10]. We now have the following lemma.…”

“…In this section we construct a Rees quotient semigroup from Reg(ORCT n ) and show that it is an inverse semigroup. For n ⩾ p ⩾ 2, let K(n, p) = {α ∈ Reg(ORCT n ) : | Im α| ⩽ p} (10) be the two-sided ideal of Reg(ORCT n ) consisting of all elements of height less than or equal to p. Further, let…”