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. --

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