On the flat length of injective modules

Abstract

In this paper, we use the notion of strict Mittag–Leffler modules, in order to study the flat length of injective modules over a ring R. We show that the supremum of these flat lengths is closely related to the invariants silp R and spli R, which were defined by Gedrich and Gruenberg, as well as to the finitistic dimension of R and the injective length of the regular module. We also examine the special case where R=ℤG is the integral group ring of a group G.