Let R be a commutative ring with identity and c,d R with c a unit. (a)
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Let R be a commutative ring with identity and c,d ϵ R with c a unit.
(a) Show that the assignment x|→ cx + b induces a unique automorphism of R[x] that is the identity of R. What is its inverse?
(b) If D is an integral domain, then show that every automorphism of D[x] that is the identity on D is of the type described in (a).
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a Let be the map defined by x cx b We first show that is an automorphism of Rx It is clear that pres...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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