On a theorem of Stafford

Abstract

Stafford proved that every left or right ideal of the Weyl algebra A_n(K) is generated by two elements. In this paper we prove that every left or right ideal of the ring of differential operators over the field of formal Laurent series K((x_1,...,x_n)) is also generated by two elements. The same is true for the ring of differential operators over the convergent Laurent series C{{x_1,...,x_n}}. This is in accordance with the conjecture that says that in a (noncommutative) noetherian simple ring, every left or right ideal is generated by two elements.