a) f: Q- Q defined by f(x) = |x| for all x € Q. b) g: C-M₂ (R) defined by g (a + bi) = a b -b a h: Z[√2]- Z[√2] defined by h( a + b √2) =) a - b √2 b]
a) f: Q- Q defined by f(x) = |x| for all x € Q. b) g: C-M₂ (R) defined by g (a + bi) = a b -b a h: Z[√2]- Z[√2] defined by h( a + b √2) =) a - b √2 b]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 3
![3.
Kerf is a subring of R
c)
f is one-to-one if and only if Ker f= {0}
Determine whether the following mappings are ring homomorphisms:
f: Q- Q defined by f(x) = |x| for all x € Q.
a)
a
b
b)
g: C-M₂ (R) defined by g (a + bi) =
- b
a
h: Z[/2] - Z[√2] defined by h( a + b √2) =) a - b √2
b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9949b50e-c59e-4a5e-95ac-404b1c8ac983%2Fe0fcfed7-0a95-4454-974c-b8c6754c86f4%2Fzc2a0g1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
Kerf is a subring of R
c)
f is one-to-one if and only if Ker f= {0}
Determine whether the following mappings are ring homomorphisms:
f: Q- Q defined by f(x) = |x| for all x € Q.
a)
a
b
b)
g: C-M₂ (R) defined by g (a + bi) =
- b
a
h: Z[/2] - Z[√2] defined by h( a + b √2) =) a - b √2
b)
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