Title: Rota-Baxter modules toward derived functors,
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.