Abstract Algebra: Theory and Applications · Problem 20.1

Fields — Thomas Judson

Mathematics — Abstract Algebra · vector-spaces

Problem

If FF is a field, show that F[x]F[x] is a vector space over FF, where the vectors in F[x]F[x] are polynomials. Vector addition is polynomial addition, and scalar multiplication is defined by αp(x)\alpha p(x) for α∈F\alpha \in F.

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