Free inverse semigroupoids and their inverse subsemigroupoids

Show simple item record

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. Liu, Veny 2017-03-01T17:45:49Z 2017-03-01T17:45:49Z 2016
dc.identifier.other u0015_0000001_0002373
dc.identifier.other Liu_alatus_0004D_12521
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 University of Alabama. Dept. of Mathematics Mathematics The University of Alabama doctoral Ph.D.

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search DSpace


My Account