3. Are the rings 2Z, 3Z isomorphic. Any isomorphism is linear for addi- tion, so it has the form f (x) = kx. Is there some k which commutes with multiplication? Another approach is to ask if the second ring has a nonzero element y such that y? = 2y.

3. Are the rings 2Z, 3Z isomorphic. Any isomorphism is linear for addi- tion, so it has the form f (x) = kx. Is there some k which commutes with multiplication? Another approach is to ask if the second ring has a nonzero element y such that y? = 2y.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

3. Are the rings 2Z, 3Z isomorphic. Any isomorphism is linear for addi-
tion, so it has the form f(x) = kx. Is there some k which commutes with
multiplication? Another approach is to ask if the second ring has a nonzero
element y such that y? = 2y.
6.
Show tho ring Sa Iba/2lx b 7Uhag ovactly 2 9utomornhisms
Thoro

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