论文标题
在第二个Weyl代数中的理想化器
Idealizers in the Second Weyl Algebra
论文作者
论文摘要
鉴于一个正确的理想$ i $ in Ring $ r $，$ r $ $ i $ in $ i $ r $的理想化镜是$ r $的最大子来源，其中$ i $成为双面理想。在本文中，我们考虑了第二个Weyl代数$ a_2 $的理想化器，这是$ \ m athbb {k} [k} [x，y] $（特征$ 0 $）上的微分运算符环。具体而言，让$ f $是$ x $和$ y $的多项式，它定义了一种不可约束的曲线，其奇异性都是尖端。我们表明，正确的理想$ fa_2 $ in $ a_2 $的理想化合物始终是左右的noetherian，从而扩展了McCaffrey的工作。
Given a right ideal $I$ in a ring $R$, the idealizer of $I$ in $R$ is the largest subring of $R$ in which $I$ becomes a two-sided ideal. In this paper we consider idealizers in the second Weyl algebra $A_2$, which is the ring of differential operators on $\mathbb{k}[x,y]$ (in characteristic $0$). Specifically, let $f$ be a polynomial in $x$ and $y$ which defines an irreducible curve whose singularities are all cusps. We show that the idealizer of the right ideal $fA_2$ in $A_2$ is always left and right noetherian, extending the work of McCaffrey.
