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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2021 • Question 1

Question

Math 6310 • Algebra Spring 2021 • Question 1

Let \(d\) be the greatest common divisor of positive integers \(n\) and \(m\). Prove that

\[ \mathbb {Z}/(n)\otimes _{\mathbb {Z}}\mathbb {Z}/(m)\cong \mathbb {Z}/(d). \]

Raw LaTeX

Let \(d\) be the greatest common divisor of positive integers \(n\) and \(m\). Prove that

\[
\mathbb{Z}/(n)\otimes_{\mathbb{Z}}\mathbb{Z}/(m)\cong\mathbb{Z}/(d).
\]

Topic Tags

Ideals and Quotient Rings Tensor Products of Modules