A class of zero divisor rings in which every graph is precisely the union of a complete graph and a complete bipartite graph

• Autorzy: Syed Khalid Nauman , Basmah H. Shafee
• Języki publikacji: EN

Abstrakty

EN

Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor). We call a ring R to be right absorbing if for a; b in R, ab is not 0, then ab D a. We first show that right absorbing rings are generalized right Klein 4-rings of characteristic two and that these are non-commutative zero-divisor local rings. The zero-divisor graph of such a ring is proved to be precisely the union of a complete graph and a complete bipartite graph. Finally, we have estimated lower and upper bounds of the genus of such a ring.

Słowa kluczowe

EN

Right (left) absorbing rings; Klein 4-rings; Zero-divisor (di)graphs; Genus of a ring

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-02-22

zaakceptowano

2015-08-13

online

2015-09-25

Twórcy

autor

Syed Khalid Nauman

• Department of Mathematics, King Abdulaziz University, Jeddah, KSA

autor

Basmah H. Shafee

• Department of Mathematics, Umm al-Qura University, Makkah, KSA

Bibliografia

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Identyfikatory

DOI

10.1515/math-2015-0050