Exercise 2, § 2

Show that every quadratic algebra over $\mathbf{Z}$ is isomorphic to an algebra of type $(0, n)$ with $n \in \mathbf{N}$, or an algebra of type $(m, 0)$ with $m$ a non-square, or an algebra of type $(m, 1)$, where $m$ is an integer which is not of the form $k(k-1)$; moreover, no two of these algebras are isomorphic.