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International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
May 21-24, 2002
Vanderbilt University
Nashville, TN, USA

Organizers
Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote

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On the congruence problem for polynomial semirings over natural numbers
by
Olga Sokratova
University of Iowa

We apply rewriting techniques to solve the congruence problem for polynomial semirings over natural numbers. Given a relation T on N[x1, ..., xn] a reduction relation is defined. A completion procedure is given. If the procedure terminates, then for a finite relation T on N[x1, ..., xn] it gives a relation T' such that T' defines the same congruence relation as T does, and the reduction relation defined by T' is convergent. In contrast to the completion procedure for polynomial rings, this algorithm may not terminate. This is not unexpected since the congruence problem for this case is in general not solvable by using rewriting.

Date received: April 28, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajl-01.