Yıl 2018, Cilt 23, Sayı 23, Sayfalar 157 - 166 2018-01-11

Some graph on prime ideals of a commutative ring

Alpesh M. Dhorajia [1]

55 73

Let R be a commutative ring with an identity. Let Spec(R) be
the set of all prime ideals of R and Max(R) be the set of all maximal ideals
of R. Let S  Max(R). We de ne an S-proper ideal sum graph on Spec(R),
denoted by 􀀀S(Spec(R); S), as an undirected graph whose vertex set is the set
Spec(R) and, for two distinct vertices P and Q, there is an arc from P to Q,
whenever P +Q M, for some maximal idealMin S. In this paper, we prove
that the complement graph of a proper sum graph 􀀀(Spec(R); S) is complete
if and only if R is an Artinian ring. We also study some basic properties of
the graph 􀀀S(Spec(R); S) such as connectivity, girth and clique number. We
explore the in
uence of the ring theoretic properties of a commutative ring R
on the proper sum graph of R and vice versa.
Proper sum graph, Artinian ring, commutative ring
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Yazar: Alpesh M. Dhorajia

Bibtex @araştırma makalesi { ieja373659, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2018}, volume = {23}, pages = {157 - 166}, doi = {10.24330/ieja.373659}, title = {Some graph on prime ideals of a commutative ring}, key = {cite}, author = {Dhorajia, Alpesh M.} }
APA Dhorajia, A . (2018). Some graph on prime ideals of a commutative ring. International Electronic Journal of Algebra, 23 (23), 157-166. DOI: 10.24330/ieja.373659
MLA Dhorajia, A . "Some graph on prime ideals of a commutative ring". International Electronic Journal of Algebra 23 (2018): 157-166 <http://dergipark.gov.tr/ieja/issue/33727/373659>
Chicago Dhorajia, A . "Some graph on prime ideals of a commutative ring". International Electronic Journal of Algebra 23 (2018): 157-166
RIS TY - JOUR T1 - Some graph on prime ideals of a commutative ring AU - Alpesh M. Dhorajia Y1 - 2018 PY - 2018 N1 - doi: 10.24330/ieja.373659 DO - 10.24330/ieja.373659 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 157 EP - 166 VL - 23 IS - 23 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.373659 UR - http://dx.doi.org/10.24330/ieja.373659 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra Some graph on prime ideals of a commutative ring %A Alpesh M. Dhorajia %T Some graph on prime ideals of a commutative ring %D 2018 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 23 %N 23 %R doi: 10.24330/ieja.373659 %U 10.24330/ieja.373659
ISNAD Dhorajia, Alpesh M. . "Some graph on prime ideals of a commutative ring". International Electronic Journal of Algebra 23 / 23 (Ocak 2018): 157-166. http://dx.doi.org/10.24330/ieja.373659