A study of non-commutative Von-Neumann regular rings


Afzal F., Rukh S., Afzal D., Farahani M. R., Cancan M., Ediz S.

JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES, vol.42, no.7, pp.1425-1436, 2021 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.1080/02522667.2021.1896650
  • Journal Name: JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.1425-1436
  • Keywords: Regular Rings, Von-Neumann regular elements, Von-Neumann regular rings, ZERO DIVISOR GRAPH, MATRICES
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, we study the Von-Neumann regular elements of non-commutative rings M-2(Z(2)) and M-2(Z(3)). We prove that M-2(Z(2)) and M-3(Z(3)) are Von-Neumann rings. We also give code in C++ to compute Von-Neumann regular elements of M-2(Z(n)).