(a) If : R S is a homomorphism of rings, then the map :...

(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, •.. , x_n], S[x₁, . .. , X_n],

Transcribed Image Text:

φ(Σαϊx) = Σφαι)χ