Primary decomposable subspaces of $k[t]$ and Right ideals of the first Weyl algebra $A_{1}(k)$ in characteristic zero

Details Primary decomposable subspaces of $k[t]$ and Right ideals of the first Weyl algebra $A_{1}(k)$ in characteristic zero Primary decomposable subspaces of $k[t]$ and Right ideals of the first Weyl algebra $A_{1}(k)$ in characteristic zero

2010-01-12

arxiv.org/abs/1001.1809v1

Mathematics

Rings and Algebras

10 p

Scientific paper

In this article, we describe the right ideals of $A_1:=k[t,\partial]$, the first Weyl agebra, over any field $k$ of characteristic zero. For this, we define the notion of primary decomposable subspaces of $k[t]$. This description generalizes a result of Cannings and Holland obtained for an algebraically closed field $k$. Dans cet article, on d\'ecrit les id\'eaux \`a droite de $A_1$ sur un corps quelconque de caract\'eristique nulle. Pour cela on d\'efinit la notion de sous-espaces d\'ecomposables primaires de $k[t]$. Cette description g\'en\'eralise un r\'esultat de Cannings et Holland obtenu pour un corps $k$ alg\'ebriquement clos.

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