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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2010 • Question 4

Question

Math 6310 • Algebra Spring 2010 • Question 4

In the category of \(\mathbb {Z}\)-modules, is the module \(\mathbb {Q}/\mathbb {Z}\) (a) projective? (b) injective? (c) flat?

Justify your answer.

Raw LaTeX

In the category of \(\mathbb{Z}\)-modules, is the module \(\mathbb{Q}/\mathbb{Z}\) (a) projective?
(b) injective? (c) flat?

Justify your answer.

Topic Tags

Modules over PIDs Projective Modules Tor Functors and Projective Resolutions