The Simple Rings of Differential Operators

Differential operators on monomial rings

Rings of differential operators are notoriously difficult to compute. This paper computes the ring of differential operators on a Stanley-Reisner ring R. The D-module structure of R is determined. This yields a new proof that Nakai’s conjecture holds for Stanley-Reisner rings. An application to tight closure is described. @ 1999 Elsevier Science B.V. All rights reserved. AMS Clas.@cation: Prima...

Explicit Calculations in Rings of Differential Operators

— We use the notion of a standard basis to study algebras of linear differential operators and finite type modules over these algebras. We consider the polynomial and the holomorphic cases as well as the formal case. Our aim is to demonstrate how to calculate classical invariants of germs of coherent (left) modules over the sheaf D of linear differential operators over Cn. The main invariants w...

Graded cofinite rings of differential operators

In this paper we study subalgebras A of the algebra D(X) of differential operators on a smooth variety X which are big in the following sense: using the order of a differential operator, the ring D(X) is equipped with a filtration. Its associated graded algebra D(X) is commutative and can be regarded as the set of regular functions on the cotangent bundle ofX . The subalgebra A inherits a filtr...

Differential Polynomial Rings of Triangular Matrix Rings

On Computing Groebner Basis in the Rings of Differential Operators

Insa and Pauer presented a basic theory of Gröbner basis for differential operators with coefficients in a commutative ring in 1998, and a criterion was proposed to determine if a set of differential operators is a Gröbner basis. In this paper, we will give a new criterion such that Insa and Pauer’s criterion could be concluded as a special case and one could compute the Gröbner basis more effi...