On Rings of Differential Rota-Baxter Operators

Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to the integro-differential analogs of the classical Weyl algebra. These are analyzed in terms of skew polynomial rings and noncommutative Groebner bases.