2. Consider the following functions. Are these ring homomorphisms? If yes, prove it. If no, provide a counterexample. a) f: ZZ given by f(x) = 3x. b) g: R R given by g(x) = x² - c) h: Z→ M(Z) given by h(a) = [ a 8
2. Consider the following functions. Are these ring homomorphisms? If yes, prove it. If no, provide a counterexample. a) f: ZZ given by f(x) = 3x. b) g: R R given by g(x) = x² - c) h: Z→ M(Z) given by h(a) = [ a 8
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.2: Integral Domains And Fields
Problem 16E: Prove that if a subring R of an integral domain D contains the unity element of D, then R is an...
Question
![2.
Consider the following functions. Are these ring homomorphisms? If yes, prove
it. If no, provide a counterexample.
a) f: ZZ given by f(x) = 3x.
b) g: R R given by g(x) = x²
-
c) h: Z→ M(Z) given by h(a) = [
a
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F545e4110-447f-42e0-86d8-f710095b2322%2F0e06a7a3-6323-4165-9e76-a00b90517fa5%2Fu3eiq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
Consider the following functions. Are these ring homomorphisms? If yes, prove
it. If no, provide a counterexample.
a) f: ZZ given by f(x) = 3x.
b) g: R R given by g(x) = x²
-
c) h: Z→ M(Z) given by h(a) = [
a
8
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