Let R be the ring of all continuous real valued functions on the closed interval [0, 1]. Prove that the map : R→→→→R defined by Þ(f) = f* f(t)dt is a homomorphism of additve groups but NOT a ring homomorphism
Let R be the ring of all continuous real valued functions on the closed interval [0, 1]. Prove that the map : R→→→→R defined by Þ(f) = f* f(t)dt is a homomorphism of additve groups but NOT a ring homomorphism
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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4a
![(a) Let R be the ring of all continuous real valued functions on the closed interval [0, 1]. Prove that
the map
: R→→→ R defined by
$(1) = f ² 1
is a homomorphism of additve groups but NOT a ring homomorphism
f(t)dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabdd1821-d7b6-4171-a67e-edf70418727b%2F583169eb-4204-4cbf-98e1-eee3fd8f26e2%2Fdsgkzgs_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let R be the ring of all continuous real valued functions on the closed interval [0, 1]. Prove that
the map
: R→→→ R defined by
$(1) = f ² 1
is a homomorphism of additve groups but NOT a ring homomorphism
f(t)dt
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