Show that Z[2√-6] is not a unique factorization domain. (Hint:Factor 10 in two ways.) Why does this show that Z[2√-6] is not aprincipal ideal domain?
Show that Z[2√-6] is not a unique factorization domain. (Hint:Factor 10 in two ways.) Why does this show that Z[2√-6] is not aprincipal ideal domain?
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter5: Factoring Polynomials
Section5.1: Factoring Integers
Problem 2E
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Show that Z[2√-6] is not a unique factorization domain. (Hint:
Factor 10 in two ways.) Why does this show that Z[2√-6] is not a
principal ideal domain?
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