Advanced Engineering Mathematics
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
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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
Check Mark
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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