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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(choose chapter or problem)
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?
Questions & Answers
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