@article{discovery10156995,
            year = {2022},
           title = {Idealizers in the second Weyl algebra},
         journal = {Journal of Algebra},
            note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.},
           pages = {793--817},
          volume = {610},
           month = {November},
       publisher = {Elsevier BV},
            issn = {0021-8693},
        keywords = {Noetherian rings, Weyl algebras, Noncommutative rings},
             url = {https://doi.org/10.1016/j.jalgebra.2022.06.026},
        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 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 fA2 in A2 is always left and right noetherian, extending the work of McCaffrey.},
          author = {Reynolds, R}
}