Essentially Critically Compressible Modules

TL;DR

This paper introduces the concept of essentially critically compressible modules, a new class of modules characterized by essential compressibility and non-embeddability in their factor modules, expanding module theory understanding.

Contribution

It defines and explores the properties of essentially critically compressible modules, a novel class not previously studied in module theory.

Findings

Defines essentially critically compressible modules

Establishes key properties and characterizations

Differentiates from related module classes

Abstract

The main purpose of this paper is to introduce the concept of essentially critically compressible modules. We call an R-module M essentially critically compressible module if it is essentially compressible and additionally it cannot be imbedded in any of its factor module.