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On Free Products of Semigroups and a New Proof of Isbell's Zigzag Theorem

✍ Scribed by James Renshaw

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 58 KB
Volume: 251
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2002.9143

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✦ Synopsis

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.

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