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Monoid kernels and profinite topologies on the free Abelian group

Published online by Cambridge University Press:  17 April 2009

Benjamin Steinberg
Benjamin Steinberg
Affiliation:
Faculdade de Ciênciasda Universidade do Porto4099-002 Porto, Portugal e-mail: bsteinbg@agc0.fc.up.pt
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Abstract

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To each pseudovariety of Abelian groups residually containing the integers, there is naturally associated a profinite topology on any finite rank free Abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can effectively compute membership in the closure of a subgroup and, more generally, in the closure of a rational subset of such a free Abelian group. Several applications to monoid kernels and finite monoid theory are discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 391 - 402
Copyright
Copyright © Australian Mathematical Society 1999

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