Problem 2. Prove that R = Q(√2, √√3)= {a+b√2+c√3+d√√б | a, b, c, d € Q} is an abelian ring with the usual operations with real numbers. Show 1+√√2+√√3+√6 is a unit. Bonus: Show R is a field.
Problem 2. Prove that R = Q(√2, √√3)= {a+b√2+c√3+d√√б | a, b, c, d € Q} is an abelian ring with the usual operations with real numbers. Show 1+√√2+√√3+√6 is a unit. Bonus: Show R is a field.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.1: Definition Of A Ring
Problem 15E: 15. Let and be elements of a ring. Prove that the equation has a unique solution.
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Transcribed Image Text:Problem 2. Prove that R = Q(√√2, √√3)= {a+b√2+c√3+d√6 | a, b, c, d €
Q} is an abelian ring with the usual operations with real numbers. Show
1+√2+√√3+√6 is a unit. Bonus: Show R is a field.
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