Yıl 2017, Cilt 21, Sayı 21, Sayfalar 198 - 216 2017-01-17

WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED

Jesse Gerald Smith Jr [1]

177 112

Let R be a commutative ring with nonzero identity and I a proper ideal of R. The ideal-based zero-divisor graph of R with respect to the ideal I, denoted by ΓI (R), is the graph on vertices {x ∈ R \ I | xy ∈ I for some y ∈ R\I}, where distinct vertices x and y are adjacent if and only if xy ∈ I. In this paper, we give a complete classification of when an ideal-based zero-divisor graph of a commutative ring is complemented or uniquely complemented based on the total quotient ring of R/I.

: Zero-divisor graph, ideal-based, complemented graph, uniquely complemented graph
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Konular Matematik ve İstatistik
Dergi Bölümü Makaleler
Yazarlar

Yazar: Jesse Gerald Smith Jr
E-posta: jesse.smith@maryvillecollege.edu

Bibtex @araştırma makalesi { ieja296332, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {21}, pages = {198 - 216}, doi = {10.24330/ieja.296332}, title = {WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED}, key = {cite}, author = {Smith Jr, Jesse Gerald} }
APA Smith Jr, J . (2017). WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED. International Electronic Journal of Algebra, 21 (21), 198-216. DOI: 10.24330/ieja.296332
MLA Smith Jr, J . "WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED". International Electronic Journal of Algebra 21 (2017): 198-216 <http://dergipark.gov.tr/ieja/issue/27921/296332>
Chicago Smith Jr, J . "WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED". International Electronic Journal of Algebra 21 (2017): 198-216
RIS TY - JOUR T1 - WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED AU - Jesse Gerald Smith Jr Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.296332 DO - 10.24330/ieja.296332 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 198 EP - 216 VL - 21 IS - 21 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.296332 UR - http://dx.doi.org/10.24330/ieja.296332 Y2 - 2016 ER -
EndNote %0 International Electronic Journal of Algebra WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED %A Jesse Gerald Smith Jr %T WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 21 %N 21 %R doi: 10.24330/ieja.296332 %U 10.24330/ieja.296332