Coflat rings and modules

Abstract

modules RR and RR are coflat. The structure of these rings is examined with emphasis on the categorical dualities that arise. Finally, with respect to FC rings, categorial equivalence is discussed. O* Background and notation* Throughout this paper R denotes an associative ring with identity 1. We denote the Jacobson radical of R by J(R) and the right (left) socle of R by Soc (RR) (Soc (RR)). The pxq matrix ring over R is denoted by M.B,tpxq (R). Every right (left) ϋJ-module is assumed to be unitary. We denote the endomorphism ring of a right (left) .ff-module, MR (BM) by End(MR) (End(RM)). The category of right (left) i2-modules is denoted by CMR (RCM) and its class of objects by ^£R (R^). A submodule N ^ M is said to be essential, denoted N^2M, if N n L Φ 0 f or all 0 Φ L ^ M. A submodule N ^ M is said to be superfluous, denoted by N < M, if K + N = M implies K = M for all K ^ M. We say