Sequentially Injective Hull of Acts Over Idempotent Semigroups

In this paper using the notion of a sequentially dense monomorphism we consider sequential injectivity (s-injectivity) for acts over a semigroup S. Among other things we describe the s-injective hull of acts over an idempotent semigroup S. We also give some classes of idempotent semigroups for the acts over which the notions of injectivity and s-injectivity coincide, and hence get the injective hull of acts over these classes of semigroups.     

Injective Hulls of Acts over Left Zero Semigroups

In this paper, using the notion of "Cauchy sequences", we study the injectivity of acts over left zero semigroups, and give some equivalent conditions to it. We see that Baer criterion is true if an identity is adjoined to the semigroup. Further, we find injective hulls of acts over left zero semigroups. We hope that the technique used here will be useful to study injectivity of acts over some other more general semigroups.     

On the Baer Criterion for Acts Over Semigroups

It is known that although the Baer Criterion for injectivity holds for modules over rings with unit, it is not true for acts over an arbitrary monoid.

Seeking a characterization for the Baer Criterion to hold for acts over a monoid, in this article, using the notion of completeness introduced by Giuli, we find some classes of monoids such that for acts over them the Baer Criterion holds.     

Maximal Dense Ideal Extensions of Locally Inverse Semigroups

Every locally inverse semigroup has a maximal dense ideal extension within the class of all locally inverse semigroups.     

Semigroups Generated by Similarity Orbits

noindent We investigate the semigroups in M _n (smallbf F) generated by the similarity orbit of single matrices. February 11, 2000     

Semigroups generated by nilpotent transformations

In a seminal paper published in 1966, John Howie characterised the elements of _x, the semigroup (under composition) of all total transformations of a set X into itself, which can be written as a product of idempotents in _x. We now initiate the study of the subsemigroup of _x, the semigroup of all partial transformations of X, which is generated by the nilpotents of _x     

Hypercyclic Semigroups Generated by Ornstein-Uhlenbeck Operators

The chaotic and hypercyclic behavior of the C ₀-semigroups of operators generated by a perturbation of the Ornstein-Uhlenbeck operator with a multiple of the identity in L²(\mathbb R^N){L^2(\mathbb {R}^N)} is investigated. Negative and positive results are presented, depending on the signs of the real parts of the eigenvalues of the matrix appearing in the drift of the operator.     

Enlargements and Coverings by Rees Matrix Semigroups

 We formulate a general condition, called an enlargement, under which a semigroup T is covered by a Rees matrix semigroup over a subsemigroup. (Received 1 February 1999; in revised form 19 May 1999)     

On Varieties Generated by Minimal Complex Semigroups

A semigroup is complex if it generates a variety the subvariety lattice of which contains an isomorphic copy of every finite lattice. It is known that a complex semigroup has at least four elements and that up to isomorphism and anti-isomorphism, there are four complex semigroups of order four. Subvarieties of the varieties generated by two of these four minimal complex semigroups have previously been described. To complete the study, we describe subvarieties of the varieties generated by the remaining two semigroups. This research was partially supported by the National Natural Science Foundation of China (No.10571077) and the Natural Science Foundation of Gansu Province (No.3ZS052-A25-017)     

由格蕴涵代数诱导的伴随半群

给出由格蕴涵代数诱导出的伴随半群及有关概念 ,详细讨论伴随半群中的元素即格蕴涵代数的左映射的性质 ,得到它们的几个等价条件。最后讨论由格蕴涵代数诱导的两个双格半群与伴随半群之间的关系 ,并证明这些半群是幂等的当且仅当它们是由格 H蕴涵代数所诱导     

Semigroups of transformations restricted by an equivalence

Suppose σ is an equivalence on a set X and let E(X, σ) denote the semigroup (under composition) of all α: X → X such that σ ⊆ α ∘ α ⁻¹. Here we characterise Green’s relations and ideals in E(X, σ). This is analogous to recent work by Sullivan on K(V, W), the semigroup (under composition) of all linear transformations β of a vector space V such that W ⊆ ker β, where W is a fixed subspace of V.     

Feller Semigroups Generated by Degenerate Elliptic Operators

This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with sticky boundary condition on various spaces of continuous functions, generalizing the previous work. More precisely we construct Feller semigroups corresponding to such a diffusion phenomenon that a Markovian particle moves continuously in the state space, sticking to the boundary.     

Representation of Numerical Semigroups by Dyck Paths

We introduce square diagrams that represent numerical semigroups and we obtain an injection from the set of numerical semigroups into the set of Dyck paths.