Let F be a field and let 0₁, 02, ..., On be distinct automorhisms of F, then it is not possible to find the elements a₁, a2, ..., a not all zero in F such that n Σa₁ i=1 a₁o; (b) = 0 for all b € F.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.1: Definition Of A Ring
Problem 19E: 19. Find a specific example of two elements and in a ring such that and .
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Let F be a field and let 0₁, 02, ..., on be distinct automorhisms of F, then it is
not possible to find the elements a₁, a2, ..., aɲ not all zero in F such that
n
Σa₁
i=1
ajo; (b)
= 0 for all b € F.
Transcribed Image Text:Let F be a field and let 0₁, 02, ..., on be distinct automorhisms of F, then it is not possible to find the elements a₁, a2, ..., aɲ not all zero in F such that n Σa₁ i=1 ajo; (b) = 0 for all b € F.
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