δ-hollow modules

الملخص EN

Let R be a commutative ring with unity and M be a non zero unitary left R-module.

M is called a hollow module if every proper submodule N of M is small (N ≪ M), i.e.

N + W ≠ M for every proper submodule W in M.

A δ-hollow module is a generalization of hollow module, where an R-module M is called δ-hollow module if every proper submodule N of M is δ-small (N δ M), i.e.

N + W ≠ M for every proper submodule W in M with M / W is singular.

In this work we study this class of modules and give several fundamental properties related with this concept.