On TNC-Rings - Zubayda M. Ibraheem; Fedaa A. Nayyef (African Journal of Advanced Pure and Applied Sciences, 2023)
This paper is a continuation of study rings relative to clean ring, where we study the concepts of 2-nil clean rings TN-Clear Ring (TNC-ring) of a noncommutative ring, which introduced by Chen and Sheibani. These rings of ours naturally generalize the nil -clean rings. we show that, if is TNC - element, then is nilpotent and , where and , such that; , when every two pair of idempotent elements are orthogonal, and we determine condition under which the TNC-ring is strongly -Regular and we show that, if is commutative local ring and is maximal ideal. Then is TNC-ring if .