Fully visible modules with the most important characteristics

Abstract

In this article, the concept of fully visible modules has been introduced, a new concept, which is defined as the module , in which all submodules are visible. Examples and properties of variety that describe the concept have been presented. In addition to the characterization that represent other images equivalent to the definition has been demonstrated. Also, the direct sum of two fully visible modules has been studied.

Subject Classification:

• Primary 16D10
• Secondary 16D90

Keywords:

• Fully visible module
• Finitely generated module
• Fully invariant submodule
• Duo module
• F-regular module
• Multiplication module