Let a finite semilattice S be a chain under its natural order. We show that if a semigroup T divides a semigroup of full order preserving transformations of a finite chain, then so does any semidirect product S o T .

In this paper we introduce the notions of pure ideals, weakly pure ideals in ternary semigroups. We also de ne purely prime ideals of a ternary semigroup and study some properties of these ideals. The space of purely prime two-sided ideal is topologized.

Let A be a simple, separable C∗-algebra of stable rank one. We prove that the Cuntz semigroup of C(T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yield...

In this paper we describe $${\mathcal {R}}$$ -unipotent semigroups being regular extensions of a left band by an $$\mathcal {R}$$ semigroup T as certain subsemigroups wreath product T. We obtain Szendrei’s result that each E-unitary is embeddable into semidirect group. Further, specialising the first author’s notion $$\lambda $$ -semidirect locally semigroup, provide answer to open question rai...

and Applied Analysis 3 In 15 the asymptotic behavior of 1.1 was studied and it was proven the existence of a global attractor for the semigroup associated to 1.1 , that is, the semigroup of operators defined as S t : u0 ∈ H −→ u t ∈ H, 1.4 The main tool in proving the existence of a global attractor is to show the existence of an absorbing set inH2 I see Theorem 1.1 in 1 . Theorem 1.1 see 15 . ...

We will give a pure combinatorial proof of the Eisenbud-Goto conjecture for arbitrary monomial curves. In addition to this, we show that the conjecture holds for certain simplicial affine semigroup rings.

We show that any Hermiticity and trace preserving continuous semigroup {γt}t>0 in d dimensions is completely positive if and only if the semigroup {γt⊗ γt}t>0 is positivity preserving.

and Applied Analysis 3 Here are some useful examples of regularized quasi-semigroups. Example 2.2. Let {Tt}t≥0 be an exponentially bounded strongly continuous C-semigroup on Banach space X, with the generator A. Then K s, t : Tt, s, t ≥ 0, 2.5 defines a C-quasi-semigroup with the generator A s A, s ≥ 0, and so D D A . Example 2.3. Let X BUC R , the space of all bounded uniformly continuous func...

The variant of a semigroup S with respect to an element a ∈ S, denoted S, is the semigroup with underlying set S and operation ? defined by x ? y = xay for x, y ∈ S. In this article, we study variants T a X of the full transformation semigroup TX on a finite set X. We explore the structure of T a X as well as its subsemigroups Reg(T a X) (consisting of all regular elements) and E X (consisting ...

This paper provides short proofs of two fundamental theorems of finite semigroup theory whose previous proofs were significantly longer, namely the two-sided Krohn-Rhodes decomposition theorem and Henckell's aperiodic pointlike theorem, using a new algebraic technique that we call the merge decomposition. A prototypical application of this technique decomposes a semigroup $T$ into a two-sided s...