On TNC-Rings

Authors

  • Zubayda M. Ibraheem Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq
  • Fedaa A. Nayyef Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

Keywords:

Clean Ring, Local Ring, Nil-Clean Ring, TNC-Ring

Abstract

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 .

 

 

Author Biographies

Zubayda M. Ibraheem, Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

 

 

Fedaa A. Nayyef, Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

 

 

Dimensions

Published

2023-05-06

How to Cite

Zubayda M. Ibraheem, & Fedaa A. Nayyef. (2023). On TNC-Rings. African Journal of Advanced Pure and Applied Sciences (AJAPAS), 2(2), 126–130. Retrieved from https://aaasjournals.com/index.php/ajapas/article/view/342

Issue

Volume 2, Issue 2, April-June 2023

Section

Articles
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