
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Number 20
![ms, then the
are rings, and if o :
composite function o : R -→ R" is a homomorphism. (Use Exercise 49 of Section 13.)
20. Let R be a commutative ring with unity of prime characteristic p. Show that the map Op : R → R given hy
Op(a) = aP is a homomorphism (the Frobenius homomorphism).
21. Let R and R' be rings and let o : R → R' be a ring homomorphism such that o[R] 7 {0}. Show that if R has
unity 1 and R has no 0 divisors, then (1) is unity for R'.
22. Let ø : R → R' he a ring ho
hom](https://content.bartleby.com/qna-images/question/b4dd8e23-ab66-4b24-8e54-a64daec9031c/493af593-9ffd-4f9e-96fc-dd2dee2adf11/ut7k7lz_thumbnail.jpeg)
Transcribed Image Text:ms, then the
are rings, and if o :
composite function o : R -→ R" is a homomorphism. (Use Exercise 49 of Section 13.)
20. Let R be a commutative ring with unity of prime characteristic p. Show that the map Op : R → R given hy
Op(a) = aP is a homomorphism (the Frobenius homomorphism).
21. Let R and R' be rings and let o : R → R' be a ring homomorphism such that o[R] 7 {0}. Show that if R has
unity 1 and R has no 0 divisors, then (1) is unity for R'.
22. Let ø : R → R' he a ring ho
hom
Expert Solution

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Step 1
Homomorphic ring means F:R---->R' and a, b belongs to R then
f(a+b) = f(a)+(b) and
f(ab) = f(a) * f(b)
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