1. Factoriality and the Pin-Reutenauer procedure
- Author
-
J. Almeida, J. C. Costa, and M. Zeitoun
- Subjects
mathematics - group theory ,primary 20m07, secondary 20m05, 20m35, 68q70 ,Mathematics ,QA1-939 - 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.
- Published
- 2016
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