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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2010 • Question 7

Question

Math 6310 • Algebra Spring 2010 • Question 7

Let \(R\) be a commutative ring with 1. Show that every \(R\)-module is free if and only if \(R\) is a field.

Raw LaTeX

Let \(R\) be a commutative ring with 1. Show that every \(R\)-module is free if and only if \(R\) is a
field.

Topic Tags

Modules over PIDs