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International Journal of Mathematics and Mathematical Sciences
Volume 9, Issue 4, Pages 821-823
http://dx.doi.org/10.1155/S0161171286001023

An hypervaluation of a ring onto a totally ordered non-cancellative semigroup without zero divisors

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Received 17 April 1985

Copyright © 1986 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.

Abstract

In this paper we answer to a question posed by Marc KRANSER: It is possible to have a totally ordered noncancellative semigroup without zero divisors, and a ring hypervaluated by this semigroup? We were able to give a positive answer and provide an example.