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）︰2014/02/27
考試時限（分鐘）：30分鐘
試題 :
代數導論第一次小考
INTRODUCTION TO ALGEBRA II - QUIZ I
FEB 27 2014
(1) (25 points) Let D be a nonempty set of the ring Z, D={3^n5^m|n,m ∈ Z_≧0},
Please describe the ring of fractions (D^-1)Z and prove that (D^-1)Z is a
commutative ring with 1.
(2) (25 points) Let A and B be ideals in a commutative ring R with identity.
Prove that if A and B are comaximal in R, then we have the ring isomorphism
R/(AB)~R/A ×R/B.