We consider a class of non-trivial perturbations A of the degenerate OrnsteinUhlenbeck operator in R . In fact we perturb both the diffusion and the drift part of the operator (say Q and B) allowing the diffusion part to be unbounded in R . Assuming that the kernel of the matrix Q(x) is invariant with respect to x ∈ R and the Kalman rank condition is satisfied at any x ∈ R by the same m < N , a...

Fountain and Gomes have shown that any proper left ample semigroup embeds into a so-called W -product, which is a subsemigroup of a reverse semidirect product T ⋉ Y of a semilattice Y by a monoid T , where the action of T on Y is injective with images of the action being order ideals of Y. Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim o...

The known theory for an oid T shows how to find a subset T of ?T, which is a compact right topological semigroup [I]. The success of the methods in [2] for obtaining properties of-T has prompted us to see how successful they would be in another context. Thus we find (Theorem 4.8) that T cont ains copies of free semigroups on 2? generators, is an immediate consequence of the stronger resu...

We study dynamical systems given by the action $T: G \times X \to X$ of a finitely generated semigroup $G$ with identity $1$ on compact metric space $X$ continuous selfmaps and $T(1,-)={\rm id} _X$. For any finite generating set

Let S be a finite non-commutative semigroup. The commuting graph of S, denoted G(S), is the graph whose vertices are the non-central elements of S and whose edges are the sets {a, b} of vertices such that a 6= b and ab = ba. Denote by T (X) the semigroup of full transformations on a finite set X. Let J be any ideal of T (X) such that J is different from the ideal of constant transformations on ...

An analogue of the Kunz-Frobenius criterion for the regularity of a local ring in a positive characteristic is established for general commutative semigroup rings. Let S be a commutative semigroup (we always assume that S contains a neutral element), and K a field. For every m 6 Z+ the assignment x H-» x, x £ S, induces a K-endomorphism 7m of the semigroup ring R = K[S]. Therefore we can consid...

Objectives/Background: The ternary seminear ring is the generalization of and it need not be a semiring. Characterization quotient rings some structures have been analysed also studied ideals in rings. Further quasi defined discussed about their properties. Methods: Properties semiring employed to carry out this research work obtain all characterizations corresponding that Findings: We call an ...

The existence of periodic solutions for the evolution equation y′(t) + Ay(t) 3 F (t, y(t)) is investigated under considerably simple assumptions on A and F . Here X is a Banach space, the operator A is m-accretive, −A generates a compact semigroup, and F is a Carathéodory mapping. Two examples concerning nonlinear parabolic equations are presented.

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...