8th Edition

ISBN: 9781285463230

Author: Gilbert, Linda, Jimmie

Publisher: Cengage Learning,

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Textbook Question

Chapter 6.2, Problem 7E

Assume that the set S = { [ x y 0 z ] | x , y , z ∈ ℤ } is a ring with respect to matrix addition and multiplication.

Verify that the mapping θ : S → ℤ defined by θ ( [ x y 0 z ] ) = z is an epimorphism from S to ℤ .

Describe ker θ , and exhibit an isomorphism from S / ker θ to ℤ .

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Chapter 6.2, Problem 6E

Chapter 6.2, Problem 8E

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