Question: Let : R R' be a ring homomorphism and let N be an ideal of R. a. Show that [N] is an ideal

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 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 full answer

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