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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 13, Issue 1


Volume 13 (2015)

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

Syed Khalid Nauman / Basmah H. Shafee
Published Online: 2015-09-25 | DOI: https://doi.org/10.1515/math-2015-0050


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.

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


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About the article

Received: 2015-02-22

Accepted: 2015-08-13

Published Online: 2015-09-25

Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0050.

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© 2015. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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