# 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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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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Step 1

Definition of Polynomial ring-

Step 2

Yes, f(nx)=f(0)

In a ring, the characteristic is the smallest integer n such that nx=0 for all x in the ring.

Step 3

From the ab...

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