课程名称︰代数二
课程性质︰数学系选修，可抵必修代数导论二
课程教师︰林惠雯
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2017/3/20
考试时限（分钟）：50分钟
试题 :
1. Do one of the following problems.
(a) Let f(x) ∈ K[x]. Prove that a splitting field of f(x) over K exists and
is unique up to isomorphism.
(b) Let K be a field. Prove that an algebraic closure of K exists and is
unique up to isomorphism.
(c) Let K ⊂ M ⊂ L be a tower of fields. Prove that L/K is a separable
extension if and only if both L/M and M/K are separable extensions.
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2. Determine the Galois group G of the polynomial x ＋2 over Q and the
correspondence between subgroups of G and intermediate fields between Q and
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the splitting field L of x ＋2 over Q.