19. Show that if R, R', and R" are rings, and if o : R R' and : R'→ R" are homomorphisms, then the composite function yo : R→ R" is a homomorphism. (Use Exercise 49 of Section 13.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Number 19

Lb a
is an isomorphism.
18. Show that each homomorphism from a field to a ring is either one to one or maps everything onto 0.
19. Show that if R, R', and R" are rings, and if o : R R' and : R→ R" are homomorphisms, then the
composite function yo: 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 gjyen by
Onla) = (P
Transcribed Image Text:Lb a is an isomorphism. 18. Show that each homomorphism from a field to a ring is either one to one or maps everything onto 0. 19. Show that if R, R', and R" are rings, and if o : R R' and : R→ R" are homomorphisms, then the composite function yo: 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 gjyen by Onla) = (P
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