Yıl 2016, Cilt 20, Sayı 20, Sayfalar 111 - 135 2016-12-01
| | | |

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

#### David F. Anderson [1] , Elizabeth F. Lewis [2]

##### 267 277

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.
Zero-divisor, zero-divisor graph, ideal-based zero-divisor graph, compressed zero-divisor graph, congruence-based zero-divisor graph
Konular Matematik JA94JH63VM Makaleler Yazar: David F. Anderson Yazar: Elizabeth F. Lewis
 Bibtex @ { ieja266187, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2016}, volume = {20}, pages = {111 - 135}, doi = {10.24330/ieja.266187}, title = {A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING}, key = {cite}, author = {Lewis, Elizabeth F. and Anderson, David F.} } APA Anderson, D , Lewis, E . (2016). A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING. International Electronic Journal of Algebra, 20 (20), 111-135. DOI: 10.24330/ieja.266187 MLA Anderson, D , Lewis, E . "A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING". International Electronic Journal of Algebra 20 (2016): 111-135 Chicago Anderson, D , Lewis, E . "A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING". International Electronic Journal of Algebra 20 (2016): 111-135 RIS TY - JOUR T1 - A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING AU - David F. Anderson , Elizabeth F. Lewis Y1 - 2016 PY - 2016 N1 - doi: 10.24330/ieja.266187 DO - 10.24330/ieja.266187 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 111 EP - 135 VL - 20 IS - 20 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266187 UR - http://dx.doi.org/10.24330/ieja.266187 Y2 - 2018 ER - EndNote %0 International Electronic Journal of Algebra A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING %A David F. Anderson , Elizabeth F. Lewis %T A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING %D 2016 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 20 %N 20 %R doi: 10.24330/ieja.266187 %U 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 (Aralık 2016): 111-135. http://dx.doi.org/10.24330/ieja.266187