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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2007 • Question 6

Question

Math 6310 • Algebra Fall 2007 • Question 6

Show that \(\mathbb {Q}\otimes _{\mathbb {Z}}\mathbb {Q}=\mathbb {Q}\) and \(\mathbb {Q}\otimes _{\mathbb {Z}}(\mathbb {Z}/n\mathbb {Z})=0\).

Raw LaTeX

Show that \(\mathbb{Q}\otimes_{\mathbb{Z}}\mathbb{Q}=\mathbb{Q}\) and
\(\mathbb{Q}\otimes_{\mathbb{Z}}(\mathbb{Z}/n\mathbb{Z})=0\).

Topic Tags

Tensor Products of Modules