Large Small Submodules with Chain Conditions
Chained R -module
Noetherian module
Large small Submodules with ascending (respectively
descending) Chain condition
We consider R is any ring with identity and is a non-zero unitary left R-module. In this article we study the notions of large small submodules with ascending (descending) chain conditions on large small submodules. Also, we will discuss and study many basic properties about this concept that fulfills the chain condition with its generalization to the ring. Where a submodule of is said to be large small of denoted by if for such that then is essential in .