Let : R R' be a ring homomorphism and let N be an ideal of

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Let ∅ : R → R' be a ring homomorphism and let N be an ideal of R.

a. Show that ∅[N] is an ideal of ∅[R].

b. Give an example to show that ∅[N] need not be an ideal of R'.

c. Let N' be an ideal either of ∅[R] or of R'. Show that ∅^-1[N'] is an ideal of R.

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 05, 2023 05:26 AM

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Let : R R' be a ring homomorphism and let N be an ideal of

Question:

Step by Step Answer:

a Because the ideal N is also a subring of R Theorem 263 shows that N is a subring of R To show that is is an ideal of R we show that rN N and Nr N fo...View the full answer

A First Course In Abstract Algebra

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