Nearly maximal submodules

Abstract EN

In this paper we introduce the concept of nearly maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of M is called nearly maximal, if whenever a submodule W of M containing N properly implies that W+J(M)=M.

Various properties of nearly maximal submodules are considered.

Also we define an NM-module, which is a module in which every proper nonzero submodule is nearly maximal; we study some properties of this class of modules