On rings of differential Rota–Baxter operators

Abstract

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 Gröbner bases.