课程名称︰代数导论二
课程性质︰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）︰2014/02/27
考试时限（分钟）：30分钟
试题 :
代数导论第一次小考
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.