Let F be a field and let 0₁, 02, ..., on be distinct automorhisms of F, then it isnot possible to find the elements a₁, a2, ..., aɲ not all zero in F such thatnΣa₁i=1ajo; (b)= 0 for all b € F.

Let F be a field and let be distinct automorhisms of F, then we have to show that it is not…

Answered: Let F be a field and let 0₁, 02, ...,…

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, ..., a not all zero in F such that n Σa₁ i=1 a₁o; (b) = 0 for all b € F.