ON A CLASS OF MODULES WHOSE NON-ZERO ENDOMORPHISMS ARE MONOMORPHISMS

Abstract

 In this paper are established some results concerning a class of modules, denoted by M, consisting of all non-zero R-moduIes with the property that every non-zero endomorphism of A is a monomorphism. If AÎM, then A is indecomposable, End_R(A) is a domain and Ann_R a=Ann_R A for every 0¹aÎA. If R is commutative and AÎM, it is shown that Ann_R A is a prime ideal of R, A is a torsion-free R/Ann_R A-moduIe and if A is uniform then A is isomorphic to a submodule of Ann_E(R/Ann_R A)(Ann_R A).