(a) If : R S is a homomorphism of rings, then the map :...
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(a) If φ : R → S is a homomorphism of rings, then the map φ̅ : R[[x]] → S[[x]] given by is a homomorphism of rings such that φ̅ (R[x]) ⊂ S[x].
(b) φ̅ is a monomorphism [epimorphism] if and only if φ̅ is. In this case φ̅ : R[x] → S[x] is also a monomorphism [epimorphism].
(c) Extend the results of (a) and (b) to the polynomial rings R[x1, •.. , xn], S[x1, . .. , Xn],
Transcribed Image Text:
φ(Σαϊx) = Σφαι)χ
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a Step 1 Let R S be a homomorphism of rings Define the map Rx Sx by a i x i a i x i We need to show that is a homomorphism of rings such that Rx Sx Fi...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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