### On a Generalized Zero-divisor Graph of a Commutative Ring with Respect to an ideal

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

S. Akbari and A. Mohammadian, On the zero-divisor graph of a commutative ring, J. Algebra 274 (2004), 847– 855.

D. D. Anderson and M. Naseer, Beck’s coloring of a commutative ring, J. Algebra 159 (1993), 500–514.

D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), 434–447.

D. F. Anderson, A. Frazier, A. Laave and P. S. Livingston, The zero-divisor graph of a commutative ring II, Lecture notes in pure and appl. math., 220 (2001), New York/Basel:

Marcel Dekker, 61 – 72.

I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), 208–226.

P. Dheena and B. Elavarasan, An ideal-based zero-divisor graph of 2-primal near-rings, Bull. Commun. Korean Math. Soc. 46 (2009), No. 6, 1051–1060.

P. Dheena and B. Elavarasan, A generalized ideal-based zero-divisor graph of a near-ring, Commun. Korean Math. Soc. 24 (2009), No. 2, 161–169.

R. Diestel, Graph Theory, Springer-Verlag, New York (1997).

N. Herstein, Topics in Algebra, 2nd Edition, John Wiley & Sons, (Asia) Pte Ltd (1999).

H. Maimani, M. R. Pouranki and S. Yassemi, Zero-divisor graph with respect to an ideal, Communications in Algebra, Vol. 34 (2006) no. 3, 923 – 929.

S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003), No. 9, 4425– 4443.

DOI: http://dx.doi.org/10.26713%2Fcma.v8i3.355

### Refbacks

- There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905