1. Assume that the set S 1, y, z € Z is a ring with respect to matrix addition and :]}-- multiplication. (a) Verify that the mapping 0 :S Z defined by e ') - z is a ring homomorphism from S to Z. (b) Find ker e. (c) Find S/kere. (d) Find an isomorphism from S/kere to Z.
1. Assume that the set S 1, y, z € Z is a ring with respect to matrix addition and :]}-- multiplication. (a) Verify that the mapping 0 :S Z defined by e ') - z is a ring homomorphism from S to Z. (b) Find ker e. (c) Find S/kere. (d) Find an isomorphism from S/kere to Z.
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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1. Assume that the set S
r, y, z e Z is a ring with respect to matrix addition and
multiplication.
(a) Verify that the mapping 0 : S Z defined by e( ') - z is a ring homomorphism from
S to Z.
(b) Find ker 0.
(c) Find S/kere.
(d) Find an isomorphism from S/kere to Z.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02d23cc1-ce59-4441-aaff-cb2d8a483c2f%2F2654688c-9c97-42a7-beca-651466b80cb3%2Fkk5adyx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:{[i ?]
1. Assume that the set S
r, y, z e Z is a ring with respect to matrix addition and
multiplication.
(a) Verify that the mapping 0 : S Z defined by e( ') - z is a ring homomorphism from
S to Z.
(b) Find ker 0.
(c) Find S/kere.
(d) Find an isomorphism from S/kere to Z.
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