On a theorem of Stafford

2010/05/24 by Napoleon Caro, Caro, Napoleon, Daniel Levcovitz +1
Computer Science · Mathematics · #16S32 #Advanced Topics in Algebra #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1005.4427

openalex publication_date 2010/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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((x₁,...,x_n)) is also generated by two elements. The same is true for the ring of differential operators over the convergent Laurent series Cx₁,...,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.

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