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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2014 • Question 4

Question

Math 6310 • Algebra Fall 2014 • Question 4

Let \(M\) and \(N\) be finitely generated modules over a commutative local ring \(A\). If \(M\otimes _A N=0\), prove that \(M=0\) or \(N=0\). Is this true if \(A\) is not local? Prove or disprove.

Raw LaTeX

Let \(M\) and \(N\) be finitely generated modules over a commutative local ring \(A\). If
\(M\otimes_A N=0\), prove that \(M=0\) or \(N=0\). Is this true if \(A\) is not local? Prove or disprove.

Topic Tags

Tensor Products of Modules