课程名称︰代数导论二
课程性质︰数学系必修
课程教师︰庄武谚
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰106/4/6
考试时限（分钟）：30分钟
试题 :
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].