In a ring, the characteristic is the smallest integer n such that nx=0 for all x in the ring. Is it acceptable to take "f" of both sides to get: f(nx)=f(0) in the corresponding polynomial ring? If so, is f(0) 0 in the polynomial ring? And can we write f(nx) as nf(x)?

In a ring, the characteristic is the smallest integer n such that nx=0 for all x in the ring. Is it acceptable to take "f" of both sides to get: f(nx)=f(0) in the corresponding polynomial ring? If so, is f(0) 0 in the polynomial ring? And can we write f(nx) as nf(x)?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 13E

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In a ring, the characteristic is the smallest integer n such that nx=0 for all x in the ring. Is it acceptable to take "f" of both sides to get:

f(nx)=f(0) in the corresponding polynomial ring?

If so, is f(0) 0 in the polynomial ring?

And can we write f(nx) as nf(x)?

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