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A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING

Year 2016, , 111 - 135, 01.12.2016
https://doi.org/10.24330/ieja.266187

Abstract

Let R be a commutative ring with 1 6= 0, I a proper ideal of R,
and ∼ a multiplicative congruence relation on R. Let R/∼ = { [x]∼ | x ∈
R } be the commutative monoid of ∼-congruence classes under the induced
multiplication [x]∼[y]∼ = [xy]∼, and let Z(R/∼) be the set of zero-divisors of
R/∼. The ∼-zero-divisor graph of R is the (simple) graph Γ∼(R) with vertices
Z(R/∼) \{[0]∼} and with distinct vertices [x]∼ and [y]∼ adjacent if and only
if [x]∼[y]∼ = [0]∼. Special cases include the usual zero-divisor graphs Γ(R)
and Γ(R/I), the ideal-based zero-divisor graph ΓI (R), and the compressed
zero-divisor graphs ΓE(R) and ΓE(R/I). In this paper, we investigate the
structure and relationship between the various ∼-zero-divisor graphs.

Year 2016, , 111 - 135, 01.12.2016
https://doi.org/10.24330/ieja.266187

Abstract

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Details

Subjects Mathematical Sciences
Other ID JA94JH63VM
Journal Section Articles
Authors

David F. Anderson This is me

Elizabeth F. Lewis This is me

Publication Date December 1, 2016
Published in Issue Year 2016

Cite

APA Anderson, D. F., & Lewis, E. F. (2016). A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING. International Electronic Journal of Algebra, 20(20), 111-135. https://doi.org/10.24330/ieja.266187
AMA Anderson DF, Lewis EF. A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING. IEJA. December 2016;20(20):111-135. doi:10.24330/ieja.266187
Chicago Anderson, David F., and Elizabeth F. Lewis. “A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING”. International Electronic Journal of Algebra 20, no. 20 (December 2016): 111-35. https://doi.org/10.24330/ieja.266187.
EndNote Anderson DF, Lewis EF (December 1, 2016) A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING. International Electronic Journal of Algebra 20 20 111–135.
IEEE D. F. Anderson and E. F. Lewis, “A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING”, IEJA, vol. 20, no. 20, pp. 111–135, 2016, doi: 10.24330/ieja.266187.
ISNAD Anderson, David F. - Lewis, Elizabeth F. “A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING”. International Electronic Journal of Algebra 20/20 (December 2016), 111-135. https://doi.org/10.24330/ieja.266187.
JAMA Anderson DF, Lewis EF. A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING. IEJA. 2016;20:111–135.
MLA Anderson, David F. and Elizabeth F. Lewis. “A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING”. International Electronic Journal of Algebra, vol. 20, no. 20, 2016, pp. 111-35, doi:10.24330/ieja.266187.
Vancouver Anderson DF, Lewis EF. A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING. IEJA. 2016;20(20):111-35.