Grading and Filtrations of Gamma Rings

TL;DR

This paper introduces and explores graded and filtered gamma rings and modules, establishing their relationships and properties, including the concept of strongly graded gamma rings, to advance the algebraic theory of gamma structures.

Contribution

It presents the first comprehensive study of graded and filtered gamma rings and modules, including their construction, properties, and the notion of strongly graded gamma rings.

Findings

Filtered gamma rings generalize graded rings.

A graded gamma ring can be constructed from a filtered gamma ring.

Properties of graded and filtered gamma rings are systematically investigated.

Abstract

The aim of this paper is to introduce and study graded and filtered gamma rings and gamma modules. We prove that the filtered $\Gamma$-ring (module) is a generalization of the notion of graded ring (module). Also, we construct a graded $\Gamma$-ring from a filtered $\Gamma$-ring. We investigate some properties of graded and fileterd Gamma rings and Gamma modules. Finally we define and study the strongly graded gamma rings.