Generalization of Flat Module Over Non-Commutative Ring

This study enhances the study of module approximation over commutative rings to module approximation over general rings. Free, torsion free, projective, flat approximations and approximations by modules embeddable in a flat module appear in literature. In this study a slightly different concept of I-flat modules is utilized to study approximations. Covers by I-flat modules and modules embeddable in I-flat modules are thus studied in the newer set up. Also, the links between flat and I-flat covers are explored. In modern literature the terminology of approximation is some times replaced by the terminology of cover. Throughout this study it is preferred to adopt the same.

A ring A to be imbedded in a ring D, the study deals with D-flat and D(n)-flat modules where D-flat modules are defined in terms of D-cotorsion modules. By using D-flat modules, D-approximations are studied. Then D(n)-flat modules are introduced as a generalization of D-flat modules. A theory for D(n)-approximations is developed accordingly.