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2015 | 13 | 1 |
Tytuł artykułu

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

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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.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-02-22
zaakceptowano
2015-08-13
online
2015-09-25
Twórcy
Bibliografia
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  • [4] Wang Hsin-Ju, Zero-divisor graphs of genus one, J. Algebra, 304 (2006), 666-678.
  • [5] Wickham C., Rings whose zero-divisor graphs have positive genus, J. Algebra, 321 (2009), 377-383.
  • [6] Wu T., On directed zero-divisor graphs of finite rings, Discrete Math. 296 (2005) 73-86.[WoS]
  • [7] Bell H.E., Near-rings, in which every element is a power of itself, Bull. Aust. Math. Soc. 2. (1970) 363-368.
  • [8] Cohn P.M., Reversible rings, Bull. London Math. Soc. 31, No. 6, (1999), 641-648.
  • [9] Lambek J., On the representation of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971) 359-368.
  • [10] Marks G., A taxonomy of 2-primal rings, J. Algebra, 266, (2003), 494-520.
  • [11] Marks G., Duo rings and Ore extensions, J. Algebra, 280, (2004) 463-471.
  • [12] Shafee B.H., Nauman S.K., On extensions of right symmetric rings without identity, Adv. Pure Math., (2014) 4, 665-673.
  • [13] Mohar B., Thomassen C., Graphs on Surfaces, Johns Hopkins University Press, Baltimore, 2001.
  • [14] White A. T., Graphs, Groups, and Surfaces, North-Holland, Amsterdam, 1973.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0050
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