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1. Let R be the ring of all functions f: R → R, with operations of pointwise addition and multiplication. Which of the following subsets are ideals? (a) I₁ = {ƒ € R: f(1) = 0}. (b) I₂ = {f € R: f(1) = 0 or f(2)=0}. (c) I3 = {f € R: f(1) = f(2)}.

1. Let R be the ring of all functions f: R → R, with operations of pointwise addition and multiplication. Which of the following subsets are ideals? (a) I₁ = {ƒ € R: f(1) = 0}. (b) I₂ = {f € R: f(1) = 0 or f(2)=0}. (c) I3 = {f € R: f(1) = f(2)}.

Advanced Engineering Mathematics
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. Let R be the ring of all functions f: R → R, with operations of pointwise addition and multiplication. Which of the following subsets are ideals? (a) I₁ = {ƒ € R: ƒ(1) = 0}. (b) I₂ = {ƒ € R: ƒ(1) = 0 or ƒ(2) = 0}. (c) I3 = {f € R: ƒ(1) = ƒ(2)}.
Transcribed Image Text:1. Let R be the ring of all functions f: R → R, with operations of pointwise addition and multiplication. Which of the following subsets are ideals? (a) I₁ = {ƒ € R: ƒ(1) = 0}. (b) I₂ = {ƒ € R: ƒ(1) = 0 or ƒ(2) = 0}. (c) I3 = {f € R: ƒ(1) = ƒ(2)}.
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