Free weighted (modified) differential algebras, free (modified) Rota-Baxter algebras and Gr\"{o}bner-Shirshov bases

Abstract

In this paper, we obtain respectively some new linear bases of free unitary (modified) weighted differential algebras and free nonunitary (modified) Rota-Baxter algebras, in terms of the method of Gr\"{o}bner-Shirshov bases.