課程名稱︰代數導論二
課程性質︰必修
課程教師︰莊武諺
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/05/01
考試時限（分鐘）：30分鐘
試題 :
代數導論第四次小考
INTRODUCTION TO ALGEBRA II - QUIZ IV
MAY 1 2014
(1) (15 points) Please compute the degree of α = [2+(2^1/3)]^1/2 over Q.
Is α constructible from a serise of straightedge-compass constructions?
What is the reason?
_ _
(2) (15 points) Show that Q is not a finite extension over Q. (Q is defined to
be the set of elements in C, algebraic over Q.)
(3) (20 points) Show that if [F(α):F] is odd, then F(α) = F(α^2).