In this brief talk, I introduce Archimedean Riesz spaces, also known as vector lattices, and their Archimedean Riesz space tensor product as defined by Fremlin. I define what it means to be an ideal in a Riesz space, then provide a counterexample to the statement “the Fremlin tensor product of ideals is an ideal.” Specifically, there exists an ideal $I$ in an Archimedean Riesz space $E$ such that the Fremlin tensor product of $I$ with itself is not an ideal in the Fremlin tensor product of $E$ with itself.