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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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.
|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
|Date Deposited:||12 May 2006|
|Last Modified:||31 May 2011 23:51|
|Contributors:||Renshaw, James (Author)
|Date:||1 May 2002|
|Contact Email Address:||J.H.Renshaw@maths.soton.ac.uk|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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