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Let P be a prime number. Let Zp) be the following subset of Q: a Z(p) = {₁ where a € Z, bЄ N, such that p does not divide b}. b' (a) Show that Z(p) is a ring (under operations of addition and multiplication of rational numbers). (b) Show that the ideal (p) of Z() generated by p is a maximal ideal.

Let P be a prime number. Let Zp) be the following subset of Q: a Z(p) = {₁ where a € Z, bЄ N, such that p does not divide b}. b' (a) Show that Z(p) is a ring (under operations of addition and multiplication of rational numbers). (b) Show that the ideal (p) of Z() generated by p is a maximal ideal.

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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2. Let P be a prime number. Let Z) be the following subset of Q: Z (p) (a) Show that Zp) is a ring (under operations of addition and multiplication of rational numbers). (b) Show that the ideal (p) of Z(p) generated by p is a maximal ideal. a {, where a € Z,b ≤ N, such that p does not divide b}.
Transcribed Image Text:2. Let P be a prime number. Let Z) be the following subset of Q: Z (p) (a) Show that Zp) is a ring (under operations of addition and multiplication of rational numbers). (b) Show that the ideal (p) of Z(p) generated by p is a maximal ideal. a {, where a € Z,b ≤ N, such that p does not divide b}.
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