Characteristics of Rota–Baxter algebras

Abstract

The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota–Baxter algebra, called the Rota–Baxter characteristic. We introduce an invariant, called the ascent set, of a Rota–Baxter characteristic, which allows us to classify Rota–Baxter characteristics in the homogenous case and relate Rota–Baxter characteristics in general to the homogeneous case through initial ideals. A more detailed study is given to Rota–Baxter characteristics with special base rings, including prime Rota–Baxter characteristics and the principle generation of Rota–Baxter characteristics.