International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 15-28

On block irreducible forms over Euclidean domains

W. Edwin Clark and J. J. Liang

Department of Mathematics, University of South Florida, Tampa 33620, Florida, USA

Received 11 December 1978

Copyright © 1980 W. Edwin Clark and J. J. Liang. 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.


In this paper a general canonical form for elements in a ring Euclidean with respect to a real valuation is established. It is also shown that this form is unique and minimal thus gives the arithmetical weight of an element with respect to a radix.