2. Given f is a homomorphism from the ring (R,+, ) onto the ring (R',+', '), prove that a) if (I,+, ·) is a maximal ideal of (R,+, ·), then the triple (f(I),+', ') is a maximal ideal of (R',+', '), b) if (I', +', ') is a maximal ideal of (R',+', '), then the triple (f-'(I'),+, ·) is a maximal ideal of (R. +. :).

2. Given f is a homomorphism from the ring (R,+, ) onto the ring (R',+', '), prove that a) if (I,+, ·) is a maximal ideal of (R,+, ·), then the triple (f(I),+', ') is a maximal ideal of (R',+', '), b) if (I', +', ') is a maximal ideal of (R',+', '), then the triple (f-'(I'),+, ·) is a maximal ideal of (R. +. :).

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

2. Given f is a homomorphism from the ring (R,+, ) onto the ring (R',+', '),
prove that
a) if (I,+, ) is a maximal ideal of (R,+, ·), then the triple (f(I),+', ') is a
maximal ideal of (R',+', '),
b) if (I', +', ') is a maximal ideal of (R',+', '), then the triple (f-'(1'),+, ·)
is a maximal ideal of (R, +, :).

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