作者tommyxu3 (fascination)
看板NTU-Exam
标题[试题] 105上 林惠雯 代数一 第三次小考
时间Fri Jan 13 21:06:25 2017
课程名称︰代数(一)
课程性质︰数学系选修 可抵必修代数导论(一)
课程教师︰林惠雯教授
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰105.12.05
考试时限（分钟）：50 minutes
试题 :
1.
Let F be a field with char(F) ≠ 2 and V be a vector space over F with dimV = n. Show that if f is a symmetric bilinear form on V, then there is a basis β for V such that the matrix representation of f with respet to β is diagonal.
2.
Let R be a ommutative ring with 1 and M, N be two R-modules. Show that M(tensor_R)N exists and is unique up to isomorphism.
3.
Let G be a finitely generated abelian group. Show that Q(tensor_Z)G is a finite dimensional vector space over Q.
4.
Let R be a commutative ring with 1 and I be an ideal of R. Show that if N is an R-module, then R/I(tensor_R)N is isomorphic to N/IN.
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正妹也不过就是一组物质波方程式的特解罢了
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