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)?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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