Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this paper, it was shown that the inversion of a continuous semigroup operation in a countably compact Hausdorff space is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, and (3) S is topologically regular and the square S × S is regular.
Abstract: Let S be a countably compact Hausdorff space endowed with a continuous semigroup operation turning S into an inverse semigroup. It is shown that the inversion inv : x ↦ x-1 in S is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, (3) the semigroup S is Clifford, topologically periodic and the square S × S is regular and countably compact. These results are close to the best possible since there is an example of a quasi-regular sequentially compact commutative inverse topological semigroup with discontinuous inversion.
15 citations
•
TL;DR: In this paper, the authors studied the algebraic structure of the compact right-topological semigroup λ(X) consisting of maximal linked systems on a group given a group $X$ and constructed a faithful representation of this semigroup in the semigroup of all self-maps of the power set.
Abstract: Given a group $X$ we study the algebraic structure of the compact right-topological semigroup $\lambda(X)$ consisting of maximal linked systems on $X$. This semigroup contains the semigroup $\beta(X)$ of ultrafilters as a closed subsemigroup. We construct a faithful representation of the semigroup $\lambda(X)$ in the semigroup of all self-maps of the power-set of $X$ and using this representation describe the structure of minimal ideal and minimal left ideals of $\lambda(X)$ for each twinic group $X$. The class of twinic groups includes all amenable groups and all groups with periodic commutators but does not include the free group with two generators.
15 citations
••
15 citations
••
TL;DR: In this article, the authors prove the κ-tameness of pseudovarieties N, D, K and LI, where κ is the signature comprising semigroup multiplication and the omega implicit operation.
Abstract: Tameness is a strong property of semigroup pseudovarieties related to the membership problem. Let κ be the signature comprising semigroup multiplication and the omega implicit operation. We prove the κ-tameness of the pseudovarieties N, D, K and LI.
15 citations
••
TL;DR: The notions of synchronization and simplification with respect to a given subsemigroup P of a semigroup S in terms of the syntactic semigroup of P are described to give a unified account of several theorems previously published.
15 citations