Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this article, a semigroup variety is called a variety of degree ≤ 2 if all its nilsemigroups are semigroups with zero multiplication and if all semigroup varieties of degree > 2 have zero multiplication unless they are upper-modular elements of the lattice.
Abstract: A semigroup variety is called a variety of degree ≤2 if all its nilsemigroups are semigroups with zero multiplication, and a variety of degree >2 otherwise. We completely determine all semigroup varieties of degree >2 that are upper-modular elements of the lattice of all semigroup varieties and find quite a strong necessary condition for semigroup varieties of degree ≤2 to have the same property.
23 citations
••
23 citations
••
TL;DR: In this article, the authors considered finitely generated free semigroup actions on a compact metric space and obtained quantitative information on Poincare recurrence, average first return time and hitting frequency for the random orbits induced by the semigroup action.
Abstract: We consider finitely generated free semigroup actions on a compact metric space and obtain quantitative information on Poincare recurrence, average first return time and hitting frequency for the random orbits induced by the semigroup action. Besides, we relate the recurrence to balls with the rates of expansion of the semigroup generators and the topological entropy of the semigroup action. Finally, we establish a partial variational principle and prove an ergodic optimization for this kind of dynamical action.
23 citations
•
TL;DR: In this article, the structure of the Cuntz semigroup of certain C(X,A)-algebras is analyzed in terms of semigroup valued lower semicontinuous functions.
Abstract: In this paper we analyse the structure of the Cuntz semigroup of certain $C(X)$-algebras, for compact spaces of low dimension, that have no $\mathrm{K}_1$-obstruction in their fibres in a strong sense. The techniques developed yield computations of the Cuntz semigroup of some surjective pullbacks of C$^*$-algebras. As a consequence, this allows us to give a complete description, in terms of semigroup valued lower semicontinuous functions, of the Cuntz semigroup of $C(X,A)$, where $A$ is a not necessarily simple C$^*$-algebra of stable rank one and vanishing $\mathrm{K}_1$ for each closed, two sided ideal. We apply our results to study a variety of examples.
23 citations