Free inverse semigroupoids and their inverse subsemigroupoids

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dc.contributor Dixon, Martyn R.
dc.contributor Evans, Martin J.
dc.contributor Lewis, Drew
dc.contributor Trace, Bruce S.
dc.contributor Xu, Nuo
dc.contributor.advisor Corson, Jon M.
dc.contributor.author Liu, Veny
dc.date.accessioned 2017-03-01T17:45:49Z
dc.date.available 2017-03-01T17:45:49Z
dc.date.issued 2016
dc.identifier.other u0015_0000001_0002373
dc.identifier.other Liu_alatus_0004D_12521
dc.identifier.uri https://ir.ua.edu/handle/123456789/2693
dc.description Electronic Thesis or Dissertation
dc.description.abstract Semigroupoids are generalizations of semigroups and of small categories. In general, the quotient of a semigroupoid by a congruence is not a semigroupoid and homomorphisms of semigroupoids can also behave badly. We define certain types of congruences and homomorphisms that avoid this problem. We then investigate inverse semigroupoids which are semigroupoids in which each element has a unique inverse. A free inverse semigroupoid has a (symmetric) basis, and it turns out to be unique. Using the immersion of graphs from Stallings folding, we introduce the Stallings kernel. We use this to study the structure of free inverse semigroupoids and their inverse subsemigroupoids. We show that closed inverse subsemigroupoids of a free inverse semigroupoid are to some extent similar to subgroups of a free group. In particular, there are analogues of the Nielsen-Schreier theorem and Howson's theorem. In contrast to the situation in a free group, every finitely generated closed inverse subsemigroupoid of a free inverse semigroupoid $F$ has finite index (whether or not $F$ is finitely generated).
dc.format.extent 85 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Mathematics
dc.title Free inverse semigroupoids and their inverse subsemigroupoids
dc.type thesis
dc.type text
etdms.degree.department University of Alabama. Dept. of Mathematics
etdms.degree.discipline Mathematics
etdms.degree.grantor The University of Alabama
etdms.degree.level doctoral
etdms.degree.name Ph.D.


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