NeutroAlgebra of Idempotents in Group Rings

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.

Keywords

• symmetric group
• neutroalgebra; antialgebra
• group ring
• neutrosubalgebra
• partial algebra