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Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.2: Ring Homomorphisms
Problem 29E: 29. Assume that is an epimorphism from to . Prove the following statements. If is an ideal of then...
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Number 22c

ring
unity 1 and R has no 0 divisors, then o(1) is unity for R'.
22. Let o : R → R' be a ring homomorphism and let N be an ideal of R.
a. Show that ¢[N]is an ideal of o[R].
b. Give an example to show that o[N] need not be an ideal of R'.omod i
c. Let N' be an ideal either of ø[R] or of R'. Show that o[N'] is an ideal of R.
|
23. Let F be a field, and let S he any subret of E
Transcribed Image Text:ring unity 1 and R has no 0 divisors, then o(1) is unity for R'. 22. Let o : R → R' be a ring homomorphism and let N be an ideal of R. a. Show that ¢[N]is an ideal of o[R]. b. Give an example to show that o[N] need not be an ideal of R'.omod i c. Let N' be an ideal either of ø[R] or of R'. Show that o[N'] is an ideal of R. | 23. Let F be a field, and let S he any subret of E
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