Suppose \(A\) is a finitely generated abelian group such that \(A\otimes _{\mathbb {Z}}\mathbb {F}=0\) for all finite fields \(\mathbb {F}\). Show that \(A=0\).
Question
Math 6310 • Algebra
Spring 2017 • Question 3
Question
Spring 2017 • Question 3
Suppose \(A\) is a finitely generated abelian group such that \(A\otimes _{\mathbb {Z}}\mathbb {F}=0\) for all finite fields \(\mathbb {F}\). Show that \(A=0\).