Let p be a prime number. Let Z(p) be the following subset of Q: a where a € Z, b E N, such that p does not divide b}. b' Z(p) = (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(p) generated by p is a maximal ideal.
Let p be a prime number. Let Z(p) be the following subset of Q: a where a € Z, b E N, such that p does not divide b}. b' Z(p) = (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(p) generated by p is a maximal ideal.
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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