NeutroAlgebra of Idempotents in Group Rings

Authors

  • Vasantha Kandasamy School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India
  • Ilanthenral Kandasamy School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India

Keywords:

Symmetric group, NeutroAlgebra, AntiAlgebra, group ring, NeutrosubAlgebra, Partial Algebra

Abstract

In this paper, the authors study the new concept of NeutroAlgebra of idempotents in group rings. It is assumed that RG is the group ring of a group G over the ring R. R should be a commutative ring with unit 1. G can be a finite or an infinite order group which can be commutative or non-commutative. We obtain
conditions under which the idempotents of the group rings ZG, ZnG, and QG form a NeutroAlgebra under the operations + or ×. Some collection of idempotents in these group rings form an AntiAlgebra. We propose some open problems which has resulted from this study.

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Published

2022-06-01

Issue

Vol. 50 (2022): Neutrosophic Sets and Systems

Section

SI#1,2024: Neutrosophical Advancements And Their Impact on Research

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

 Creative Commons Attribution (CC BY) license.

How to Cite

Kandasamy, V. ., & Kandasamy, I. . (2022). NeutroAlgebra of Idempotents in Group Rings. Neutrosophic Sets and Systems, 50, 156-177. http://fs.unm.edu/nss8/index.php/111/article/view/2516