Rota-Baxter modules toward derived functors

TL;DR

This paper explores Rota-Baxter modules, highlighting the impact of Rota-Baxter operators and establishing foundational concepts like free, projective, injective, and flat modules to facilitate derived functor computations.

Contribution

It introduces the theory of Rota-Baxter modules, including constructions and properties, enabling the development of resolutions for derived functors.

Findings

Construction of free Rota-Baxter modules

Existence of enough projective, injective, and flat modules

Framework for derived functor resolutions

Abstract

In this paper we study Rota-Baxter modules with emphasis on the role played by the Rota-Baxter operators and resulting difference between Rota-Baxter modules and the usual modules over an algebra. We introduce the concepts of free, projective, injective and flat Rota-Baxter modules. We give the construction of free modules and show that there are enough projective, injective and flat Rota-Baxter modules to provide the corresponding resolutions for derived functor.