On FI-cotorsion modules and dimensions

Abstract

In this paper we study the class of FI-cotorsion modules and we introduce there dimensions of modules and rings. An R-module M is called FI-cotorsion if Ext¹_R(F,M) = 0 for any FI-flat R-module F. Also, we investigate some properties of FI-cotorsion modules and FI-cotorsion envelopes and we give a characterization of IF-ring. Then, we study the FI-flat and the FI-cotorsion envelope and we show when they existed. Furthermore, we present the notation of FI-cotorsion dimension of modules and rings.