課程名稱︰代數導論二
課程性質︰數學系必修
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）︰106/4/6
考試時限（分鐘）：30分鐘
試題 :
1.(25 points) Let P be a prime ideal of the integral domain R and let
n n-1
f(x) = x + a x +...+ a x + a be a polynomial in R[x](here n≧1).
n-1 1 0
2
Show that if a ∈P for i = 1,...,n-1 and ﹁(a ∈P ), then f(x) is
i 0
irreducible in R[x].
2.(25 points) Let R = Q[x] and n be any positive integer. Show that
n
X - x is irreducible in R[X].