The following is based on a follow up to some of the comments from this post Exterior powers of a module contained in a field of fractions
Let $I$ be an integral domain and let $\operatorname{Frac}(I)$ denote its field of fractions http://en.wikipedia.org/wiki/Field_of_fractions.
let $\wedge^k M$ be the $k$-th exterior power of $M$ that is $T^k(V)/A^k(V)$ where $A(M)$ is the ideal generated by all $m \otimes m$ for $m \in M$ and $T^k(M) = M \otimes M \otimes \cdots \otimes M$ is tensor product of $k$ modules.
How do we show $\wedge^2 \operatorname{Frac}(I)$ is $0$?