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A PROOF OF ISBELL’S ZIGZAG THEOREM

Part of: Semigroups

Published online by Cambridge University Press:  01 April 2008

PIOTR HOFFMAN
PIOTR HOFFMAN*
Affiliation:
Warsaw University, Institute of Informatics, ul. Banacha 2, 02-097 Warszawa, Poland (email: piotrek@mimuw.edu.pl)
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Abstract

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We provide a short, intuitive proof of Isbell’s zigzag theorem.

Keywords

semigroupszigzags

MSC classification

Secondary: 20M50: Connections of semigroups with homological algebra and category theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 229 - 232
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Higgins, P. M., ‘A short proof of Isbell’s zigzag theorem’, Pacific J. Math. 144(1) (1990), 47–50.CrossRefGoogle Scholar
[2]Higgins, P. M., Techniques of Semigroup Theory (Oxford University Press, Oxford, 1992).CrossRefGoogle Scholar
[3]Howie, J. M., Fundamentals of Semigroup Theory, London Mathematical Society Monographs Series, 12 (Oxford University Press, Oxford, 1996).Google Scholar
[4]Storrer, H. H., ‘An algebraic proof of Isbell’s zigzag theorem’, Semigroup Forum 12 (1976), 83–88.CrossRefGoogle Scholar
[5]Renshaw, J., ‘On free product of semigroups and a new proof of Isbell’s zigzag theorem’, J. Algebra 251 (2002), 12–15.CrossRefGoogle Scholar
[6]Philip, J. M., ‘A proof of Isbell’s zigzag theorem’, J. Algebra 32 (1974), 328–331.CrossRefGoogle Scholar
[7]Isbell, J. R., ‘Epimorphisms and dominions’. Conference on Categorical Algebra, La Jolla, California, 1965, Proceedings, (Springer, Berlin, 1966), pp. 232–246.CrossRefGoogle Scholar
[8]Howie, J. M. and Isbell, J. R., ‘Epimorphisms and dominions II’, J. Algebra 6 (1967), 7–21.CrossRefGoogle Scholar