Duality in Noetherian rings

Abstract

Since we shall make such heavy use of this theorem and the techniques used in its proof, we shall now make the standing assumptions that every ring we consider will be both right and left Noetherian and that every module will be finitely generated. The notation and terminology will follow that of Cartan and Eilenberg [2] although we shall usually drop the ring from Hom and Ext since we shall not change rings. In this paper, we shall be concerned with several questions arising out of duality theory. In ?1 we shall consider various conditions which insure that certain modules are reflexive. A useful tool is the exact sequence 0->A--A**+Extl(B, R)-O which holds for torsion-