On free products of semigroups and a new proof of Isbell's zigzag theorem
On free products of semigroups and a new proof of Isbell's zigzag theorem
J. R. Isbell proved his famous zigzag theorem for semigroups using essentially topological methods in [Epimorphisms and dominions, in "Proceedings of the Conference on Categorical Algebra, La Jolla, 1965," pp. 232–246]. Since then a number of authors have proved this result using a variety of different techniques. We present in this paper a description of the free product of a special amalgam of monoids using the "homological" techniques introduced by the author in [Proc. London Math. Soc. (3)52 (1986), 119–141] and from this derive a short proof of the zigzag theorem. This is the first proof which makes direct use of the amalgamated free product.
amalgam, dominion, free-product, Isbell, monoid, semigroup, zigzag
12-15
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
1 May 2002
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
Renshaw, James
(2002)
On free products of semigroups and a new proof of Isbell's zigzag theorem.
Journal of Algebra, 251 (1), .
(doi:10.1006/jabr.2002.9143).
Abstract
J. R. Isbell proved his famous zigzag theorem for semigroups using essentially topological methods in [Epimorphisms and dominions, in "Proceedings of the Conference on Categorical Algebra, La Jolla, 1965," pp. 232–246]. Since then a number of authors have proved this result using a variety of different techniques. We present in this paper a description of the free product of a special amalgam of monoids using the "homological" techniques introduced by the author in [Proc. London Math. Soc. (3)52 (1986), 119–141] and from this derive a short proof of the zigzag theorem. This is the first proof which makes direct use of the amalgamated free product.
This record has no associated files available for download.
More information
Published date: 1 May 2002
Keywords:
amalgam, dominion, free-product, Isbell, monoid, semigroup, zigzag
Identifiers
Local EPrints ID: 29858
URI: http://eprints.soton.ac.uk/id/eprint/29858
ISSN: 0021-8693
PURE UUID: e9b7a827-859a-44e9-91d1-6df2430fd452
Catalogue record
Date deposited: 12 May 2006
Last modified: 16 Mar 2024 02:39
Export record
Altmetrics
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
