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

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

Öz

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.

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

Öz

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Ayrıntılar

Konular Matematik
Diğer ID JA94JH63VM
Bölüm Makaleler
Yazarlar

David F. Anderson Bu kişi benim

Elizabeth F. Lewis Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Yayımlandığı Sayı Yıl 2016

Kaynak Göster

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. Aralık 2016;20(20):111-135. doi:10.24330/ieja.266187
Chicago Anderson, David F., ve Elizabeth F. Lewis. “A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING”. International Electronic Journal of Algebra 20, sy. 20 (Aralık 2016): 111-35. https://doi.org/10.24330/ieja.266187.
EndNote Anderson DF, Lewis EF (01 Aralık 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 ve E. F. Lewis, “A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING”, IEJA, c. 20, sy. 20, ss. 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 (Aralık 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. ve Elizabeth F. Lewis. “A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING”. International Electronic Journal of Algebra, c. 20, sy. 20, 2016, ss. 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.