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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.
Emmanouil et al. (Fri,) studied this question.