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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 12, Pages 701-718

A generalised hopf algebra for solitons

1Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. Box 80015, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Wales Swansea, Wales, Swansea SA2 8PP, UK

Received 17 April 2001; Revised 22 October 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper considers a generalisation of the idea of a Hopf algebra in which a commutative ring replaces the field in the unit and counit. It is motivated by an example from the inverse scattering formalism for solitons. We begin with the corresponding idea for groups, where the concept of the identity is altered.