On free products of semigroups and a new proof of Isbell's zigzag theorem
Renshaw, James (2002) On free products of semigroups and a new proof of Isbell's zigzag theorem. Journal of Algebra, 251, (1), 12-15. (doi:10.1006/jabr.2002.9143).
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Description/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.
| Item Type: | Article |
|---|---|
| ISSNs: | 0021-8693 (print) |
| Related URLs: | |
| Keywords: | amalgam, dominion, free-product, Isbell, monoid, semigroup, zigzag |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Pure Mathematics |
| Item ID: | 29858 |
| Date Deposited: | 12 May 2006 |
| Last Modified: | 31 May 2011 23:51 |
| Contributors: | Renshaw, James (Author) |
| Date: | 1 May 2002 |
| Status: | Published |
| Contact Email Address: | J.H.Renshaw@maths.soton.ac.uk |
| URI: | http://eprints.soton.ac.uk/id/eprint/29858 |
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