ON STRONGLY C2 MODULES AND D2 MODULES

Abstract

Let R be a ring, MR be a right R-module, n be a positive integer and S = End (MR) be the endomorphism ring of MR. MR is called a strongly C2 module if [Formula: see text] is C2 for every positive integer m. MR is called an n-C2 module if the annihilator rM(K) ≠ 0 for any n-generated proper left ideal K of S. We prove that MR is strongly C2 if and only if M is n-C2 for every positive integer n, if and only if the annihilator rM(K) is not zero for every finitely generated proper left ideal K of S, and then we get some characterizations of right n-C2 rings and strongly right C2 rings. Also we obtain some dual statements of n-D2 module and strongly D2 module.