Referring to Exercise 29, let F be a field. An element of F F is a
Question:
Referring to Exercise 29, let F be a field. An element ∅ of FF is a polynomial function on F, if there exists f(x) ∈ F[x] such that ∅(a)= f(a) for all a ∈ F.
a. Show that the set PF of all polynomial functions on F forms a subring of FF.
b. Show that the ring PF is not necessarily isomorphic to F[x].
Data from Exercise 29
Let R be a ring, and let RR be the set of all functions mapping R into R. For∅, ψ ∈ RR, define the sum∅ + ψ by (∅ + ψ)(r) = ∅(r) + ψ(r) and the product ∅ . ψ by (∅ · ψ)(r) = ∅(r)ψ(r) for r ∈ R. Note that · is not function composition. Show that (RR,+,•) is a ring.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: