ON THE STRUCTURE OF COUNIFORM AND COMPLEMENTED MODULES

A module M is called complemented if, for every submodule U of M, the set {V subset-of M \ U + V = M} has a minimal element. This paper investigates the structure of complemented modules over Noetherian rings. After reducing this question to the case of local rings, we show that every complemented module is a sum of a radical minimax module and a coatomic module. Its radical component is a sum of finitely many couniform modules. The second part of this paper characterizes modules which satisfy weaker, respectively stronger, versions of being complemented, especially weakly complemented and supplemented modules.