On primary compactly packed modules

الملخص EN

A proper submodule N of a module M over a ring R is compactly packed if for each family {P } 2 of prime submodules of M with N S 2 P ,N P for some 2 .

A module M is called compactly packed if every proper submodule is compactly packed.

This concept was introduced in [17].

In this paper, we generalize this concept to primary submodules and introduce the concept of primary compactly packed modules.

We also generalize the Prime Avoidance Theorem for modules that was proved in [13] to the Primary Avoidance Theorem for modules.

In addition, we study various properties of primary compactly packed modules.