Exploring Semiprimitivity and Ideal Structures in Group Rings: A Study of K[G] and Infinite Groups

Volume 20 No 13 (2022)

Amarendra Kumar Pattanayak and Dr. Arihant Jain

DOI: 10.48047/NQ.2022.20.13.NQ88507

Abstract

In this research work, we proposed to study the group ring K[G], arising from two distinct groups G and K, is a captivating subject within algebra, bridging the gap between group theoretical and ring theoretical approaches. Despite its seemingly straightforward nature, investigating the semi-primitivity of K[G] poses unexpected challenges, particularly in determining the conditions under which the Jacobson radical of the group algebra equals zero. Understanding the ideal JK[G] structure stands as a principal objective in this study.

Keywords

Groups, Group Ring , Subgroups , Communication Rings , Near-Rings

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