On free products of semigroups and a new proof of Isbell's zigzag theorem

JOURNAL OF ALGEBRA

卷:251

Article

Renshaw, J

关键词: amalgam;    dominion;    free-product;    Isbell;    monoid;    semigroup;    zigzag;   

DOI  :  10.1006/jabr.2002.9143

来源: Elsevier

【 摘 要 】

J. R. Isbell proved his famous zigzag theorem for semigroups using essentially topological methods in [Epimorphisms and dominions, in Proccedings 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 (if 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. (C) 2002 Elesevier Science (USA).

【 授权许可】

Free