Idealizers in the Second Weyl Algebra

2020/09/23 by Reynolds, Ruth A.
#16P40 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2009.11022

Abstract

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 A₂, which is the ring of differential operators on \mathbbk[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 fA₂ in A₂ is always left and right noetherian, extending the work of McCaffrey.

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