Name
Abstract | ||
|---|---|---|
We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full. |
Year | Venue | Keywords |
|---|---|---|
2016 | DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE | pseudovariety,profinite semigroup,profinite topology,topological closure,unary implicit signature,pure implicit signature,rational language,aperiodic semigroup,Burnside pseudovariety,factorial pseudovariety,full pseudovariety,Pin-Reutenauer procedure |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Finitely-generated abelian group,If and only if,Aperiodic semigroup,Regular language,Semigroup,Free algebra,Mathematics,Free group | Journal | 18.0 |
Issue | ISSN | Citations |
3.0 | 1462-7264 | 2 |
PageRank | References | Authors |
0.46 | 11 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| josimar ribeiro de almeida | 1 | 2 | 0.46 |
| José Carlos Costa | 2 | 17 | 4.57 |
| Marc Zeitoun | 3 | 288 | 24.51 |