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Rings with a Special Kind of Automorphism

Published online by Cambridge University Press:  20 November 2018

Jeffrey Bergen  and
I. N. Herstein
Jeffrey Bergen
Affiliation:
DePaul University and University of Chicago
I. N. Herstein
Affiliation:
DePaul University and University of Chicago
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Abstract

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In this paper we examine the nature of rings R with unit having an automorphism ϕ ≠ 1 such that x — ϕ(x) is 0 or invertible for every x ∊ R. We show that the only examples of such rings are R = D, R = D2, and R = D ⊕ D, where D is a division ring. Furthermore, for the case D2, we describe the division rings that are possible.

Keywords

16A72
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 1 , 01 March 1983 , pp. 3 - 8
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Bergen, Jeffery, Herstein, I. N. and Lanski, Charles, "Derivations with invertible values", to appear in Canadian Jour. Math. Google Scholar