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 dene 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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Journal Section | Articles |
---|---|

Authors |

Bibtex | ```
@research article { ieja373659,
journal = {International Electronic Journal of Algebra},
issn = {1306-6048},
eissn = {1306-6048},
address = {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.org.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 - https://doi.org/10.24330/ieja.373659 Y2 - 2019 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 (January 2018): 157-166. https://doi.org/10.24330/ieja.373659 |