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Consider the quotient ring R = Q[x] x² − 4 > (a) Give an example of a zero divisor in R. Explain why it is a zero divisor. (b) Find -1 (x+ < x² − 4 >)¯¹in R (you should be able to see this without solving) = (c) Find (3+x)−¹ = (3+ < x² − 4 >)−¹(you can find it by solving, as - we did in class)

Consider the quotient ring R = Q[x] x² − 4 > (a) Give an example of a zero divisor in R. Explain why it is a zero divisor. (b) Find -1 (x+ < x² − 4 >)¯¹in R (you should be able to see this without solving) = (c) Find (3+x)−¹ = (3+ < x² − 4 >)−¹(you can find it by solving, as - we did in class)

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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Consider the quotient ring R = Q[x] ★ x² − 4 > (a) Give an example of a zero divisor in R. Explain why it is a zero divisor. (b) Find -1 = (x+ < x² − 4 >)¯¹in R (you should be able to see this without solving) (c) Find (3+x) we did in class) = (3+ < x² − 4 >)−¹(you can find it by solving, as
Transcribed Image Text:Consider the quotient ring R = Q[x] ★ x² − 4 > (a) Give an example of a zero divisor in R. Explain why it is a zero divisor. (b) Find -1 = (x+ < x² − 4 >)¯¹in R (you should be able to see this without solving) (c) Find (3+x) we did in class) = (3+ < x² − 4 >)−¹(you can find it by solving, as
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