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تسجيل مستخدم جديدIdealizers in the Second Weyl Algebra
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Ruth A. Reynolds
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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.
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