Modules which are invariant under automorphisms of their covers and envelopes

Projective and injective resolutions are well known tools in Algebra. It is natural to ask whether we can take other types of resolutions and how one cande fine a generalized concept of cover and envelope. We will present here an approach due to P. A. Guil Asensio, D. K. Tutuncu and A. K. Srivastava [12]. It consists in de fing a notion of chi-envelope where chi is a class of modules closed under isomorphisms. The central topic of this work is then to study the properties of modules which are invariant under automorphisms of their chi-envelopes and covers. We will then apply the results to the special cases in which the class chi is that of the injectives or the projectives.