TL;DR
This paper introduces the concept of graded gamma rings, exploring their properties, radicals, and relationships with existing graded ring theories, providing a comprehensive framework for their study.
Contribution
It generalizes the notion of gamma rings using graded ring methods and establishes equivalent perspectives and radical properties for graded gamma rings.
Findings
Introduction of graded gamma rings and their properties
Description of the graded Jacobson radical and its elements
Relationship between graded Jacobson radical and classical Jacobson radical
Abstract
We introduce graded gamma rings from a more general point of view via methods developed by Krasner and Halberstadt for graded rings. We propose three equivalent aspects of studying graded gamma rings, nonhomogeneous, semihomogeneous and homogeneous. The graded Jacobson radical of a graded gamma ring is introduced and its elementwise description is given. Also, a relation between the graded Jacobson radical and the Jacobson radical of a graded gamma ring is examined.
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Taxonomy
TopicsRings, Modules, and Algebras · Fuzzy and Soft Set Theory · Advanced Algebra and Logic