A prime submodule principle (Q2928453)

The authors introduce two notions of strongly Ako and Oka families that generalize the notions of Ako and Oka families to submodules. In the second section, the authors provide the main results of this paper. They state and prove a prime submodule principle theorem for both families and explain logical dependence between them. In the third section, they provide some applications of the results from the previous chapter. In chapter 4, the authors give relations between the family of ideals and the family of submodules. In the last section, they study the behavior of the properties in semifilter families.