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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.