Bicyclic semigroup

About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.

Derivations on Certain Semigroup Algebras

Abstract: In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

Primitive inverse semigroups of left I-quotients

Abstract: A subsemigroup $S$ of an inverse semigroup $Q$ is a left I-order in $Q$, if every element in $Q$ can be written as $a^{-1}b$ where $a, b \in S$ and $a^{-1}$ is the inverse of $a$ in the sense of inverse semigroup theory We study a characterisation of semigroups which have a primitive inverse semigroup of left I-quotients

On semigroups with an infinitesimal operator

Abstract: Let {F t : t ≥ 0} be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small t every linear selection of F t is invertible and there exists an exponential semigroup {f t : t ≥ 0} of linear continuous selections f t of F . IfX is a nonempty set, then n(X) denotes the set of all nonempty subsets of X. All linear spaces are over R. We say that a nonempty subset C of a linear space is a cone if tC ⊂ C for every t > 0. Let X, Y be linear spaces and C be a convex cone in X. The set-valued function (abbreviated to s.v. function) F : C→n(Y ) is called superadditive if F (x) + F (y) ⊂ F (x+ y) for all x, y ∈ C. (1) F is said to be additive if equality holds in (1), and Q+-homogeneous if F (λx) = λF (x) for all x ∈ C, λ ∈ Q+, (2) where Q+ is the set of all positive rational numbers. F is linear if it is additive and (2) is satisfied for all λ > 0. IfX is a linear topological space, then b(X) denotes the set of all bounded elements of n(X), and c(X) stands for the family of all compact elements of n(X). Now let X,Y be topological spaces. An s.v. function F : X → n(Y ) is called lower semicontinuous at x0 ∈ X if for every open set G in Y such that F (x0) ∩ G 6= ∅ there exists a neighbourhood U of x0 in X such that F (x) ∩ G 6= ∅ for x ∈ U . We say that F is lower semicontinuous in a set A ⊂ X if F is lower semicontinuous at every point x ∈ A. We say that F : X → n(Y ) is upper semicontinuous at x0 ∈ X if for every open set G ⊂ Y such that F (x0) ⊂ G there exists a neighbourhood U of x

Cryptic Semigroup Varieties

Abstract: We describe all minimal noncryptic periodic semigroup [monoid] varieties We prove that there are exactly three distinct maximal cryptic semigroup [monoid] varieties contained in the variety determined by xn ≈ x n+m, n ≥ 2, m ≥ 2 Analogous results are obtained for pseudovarieties: there are exactly three maximal cryptic pseudovarieties of semigroups [monoids] It is shown that if a cryptic variety or pseudovariety of monoids contains a nonabelian group, then it consists of bands of groups only Several characterizations are given of the cryptic overcommutative semigroup [monoid] varieties