Question

Asked Apr 18, 2019

Abstract Algebra. Please explain everything in detail.

Step 1

To prove the statements regarding the quotient ring F[x]/(p(x)), under the given conditions

Step 2

The first part of the problem (regarding the degree and the uniqueness of the coset representative) is a consequence of the fact that F[x] is a Euclidean domain with degree as the norm.

Step 3

We have already proved that every coset can be represented by a polynomial b(x) of degree less than the degree of p)(x). Here is the proof of the uniqueness of b(x) (for each coset). The main point is that for ...

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