abstract algebra Example 2.68In the ring R], let (x) denote the set of all polynomials that are amultiple of r, i.e. the set {rg(x) | g(x) E R[c]}.1xeExercise 2.68.2More generally, let f(x) be an arbitrary polynomial, and let (f(x))denote the set of all polynomials that are a multiple of f(x), i.e. theset {f(x)g(x) | g(x) E R[r]}. Show that (f(x)) is an ideal of R[r].

Ideal: A subset I of a ring R is called ideal if it satisfies following conditions: a) x-y∈I, ∀x,…

Answered: More generally, let f(x) be an…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 5E: Examples 5 and 6 of Section 5.1 showed that P(U) is a commutative ring with unity. In Exercises 4...

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More generally, let f(x) be an arbitrary polynomial, and let (f(x)) denote the set of all polynomials that are a multiple of f(x), i.e. the set {f(r)g(x)| g(x) E R[r]}. Show that (f(x)) is an ideal of R[r].