×

The \(k\)-zero-divisor hypergraph. (English) Zbl 1301.13006

Summary: The concept of a \(k\)-zero-divisor hypergraph of a commutative ring was introduced by Ch. Eslahchi and A. M. Rahimi [Int. J. Math. Math. Sci. 2007, Article ID 50875, 15 p. (2007; Zbl 1139.13003)]. In this paper we change the basic definitions of this concept, and we demonstrate that there are results about \(k\)-zero-divisor hypergraphs that parallel noteworthy results about zero-divisor graphs.

MSC:

13A99 General commutative ring theory
05C65 Hypergraphs

Citations:

Zbl 1139.13003
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anderson D.F., Axtell M.C., Stickles J.: Zero-divisor graphs in commutative rings. In: Fontana, M., Kabbaj, S., Olberding, B., Swanson, I. (eds) Commutative Algebra: Noetherian and Non-Noetherian Perspectives, Springer, Berlin (2010)
[2] Anderson D.F., Livingson P.S.: The zero-divisor graph of a commutative ring. J. Algebra 217, 434–447 (1999) · Zbl 0941.05062
[3] Axtell M., Coykendall J., Stickles J.: Zero-divisor graphs of polynomial and power series over commutative rings. Commun. Algebra. 33(6), 2043–2050 (2005) · Zbl 1088.13006
[4] Beck I.: Coloring of commutative rings. J. Algebra 116, 208–226 (1988) · Zbl 0654.13001
[5] Eslahchi, Ch., Rahimi, A.M.: The k-Zero-Divisor Hypergraph of a Commutative Ring. Int. J. Math. Math. Sci., Art. ID 50875, 15 pp (2007) · Zbl 1139.13003
[6] Fields E.: Zero divisors and nilpotent elements in power series rings. Proc. Am. Math. Soc. 27(3), 427–433 (1971) · Zbl 0219.13023
[7] Gilmer R., Grams A., Parker T.: Zero divisors in power series rings. Journal für die reine und ang Mathematik 278/279, 145–164 (1975) · Zbl 0309.13009
[8] Lucas T.G.: The diameter of a zero-divisor graph. J. Algebra 301, 174–193 (2006) · Zbl 1109.13006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.