1. In this exercise we will prove that Z[√-5] is an integral domain but not a unique factorisation domain (UFD). Show that for any integer m, the set Z√√m] = {a+b√√m: a, b = Z} is a subring of the field C. Use this to conclude that Z[√√m] is an integral domain.
1. In this exercise we will prove that Z[√-5] is an integral domain but not a unique factorisation domain (UFD). Show that for any integer m, the set Z√√m] = {a+b√√m: a, b = Z} is a subring of the field C. Use this to conclude that Z[√√m] is an integral domain.
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. In this exercise we will prove that Z[√-5] is an integral domain but not a
unique factorisation domain (UFD).
Show that for any integer m, the set
Z√√m] = {a+b√√m: a, b = Z}
is a subring of the field C. Use this to conclude that Z[√√m] is an integral
domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0de9773e-39c1-4df6-a7d6-864501c7f552%2F0d9d3bd5-3b40-4339-b1be-134b308e0fc0%2Fraw78j_processed.png&w=3840&q=75)
Transcribed Image Text:1. In this exercise we will prove that Z[√-5] is an integral domain but not a
unique factorisation domain (UFD).
Show that for any integer m, the set
Z√√m] = {a+b√√m: a, b = Z}
is a subring of the field C. Use this to conclude that Z[√√m] is an integral
domain.
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