# Smith Normal Form

Let $R=Z[x_{1},x_{2},\dots,x_{n}]$ be a multivariate polynomial ring. Is it possible to define a normal form for a general $m \times m$ matrix $M$ with entries from $R$?

• A normal form up to what equivalence relation? – Qiaochu Yuan Mar 8 '12 at 15:48

• Theorem $5.2$ in here seems to answer what I am asking is impossible! ams.org/journals/tran/1949-066-02/S0002-9947-1949-0031470-3/… Is my interpretation correct? – Turbo Mar 11 '12 at 7:25