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

Matthias Kouakou; Alexis Tchoudjem

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arXiv · 1001.1809

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

Matthias Kouakou·Alexis Tchoudjem

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Abstract

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 décrit les idéaux à droite de $A_1$ sur un corps quelconque de caractéristique nulle. Pour cela on définit la notion de sous-espaces décomposables primaires de $k[t]$. Cette description généralise un résultat de Cannings et Holland obtenu pour un corps $k$ algébriquement clos.

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BibTeX RIS

Matthias Kouakou, Alexis Tchoudjem. 2010-01-12. Primary decomposable subspaces of $k[t]$ and Right ideals of the first Weyl algebra $A_{1}(k)$ in characteristic zero. https://arxiv.org/abs/1001.1809

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