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Show that if e : Z --+ Z is a ring isomorphism, then e must be the identity mapping. Is

Chapter 29, Problem 29.8

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QUESTION:

Show that if e : Z --+ Z is a ring isomorphism, then e must be the identity mapping. Is therean additive group isomorphism e : Z -+ Z other than the identity mapping?

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QUESTION:

Show that if e : Z --+ Z is a ring isomorphism, then e must be the identity mapping. Is therean additive group isomorphism e : Z -+ Z other than the identity mapping?

ANSWER:

Step 1 of 2

If is a ring isomorphism, then (i) for

ii) and for

Now

Therefore,

Hence is the identity mapping

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