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Finite Rings in Which 1 is a Sum of Two Non-P-Th Power Units

Published online by Cambridge University Press:  20 November 2018

David Jacobson
David Jacobson*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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Let R be a finite ring with 1 and let R* denote the group of units of R. Let p be a prime number. In this paper we consider the question of whether there exist a, b in R* such that a and b are non- p -th powers whose sum is 1. If such units a, b existing, we say that R is an N (p)-ring. Of course if p does not divide |R*|, the order of R*, then every element in R* is a pth power.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 94 - 103
Copyright
Copyright © Canadian Mathematical Society 1976

References

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