The Annihilating-Ideal Graph of an Idealization

被引：0
|
作者：
Ahrari, M. [1 ]
Sabet, Sh. A. Safari [1 ]
Amini, B. [2 ]
机构：
[1] Islamic Azad Univ, Cent Tehran Branch, Dept Math, Tehran, Iran
[2] Shiraz Univ, Dept Math, Coll Sci, Shiraz, Iran
来源：
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE | 2017年 / 41卷 / A1期
关键词：
Annihilating-ideal graph; Idealization; Girth; Diameter;
D O I：
10.1007/s40995-017-0185-1
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The annihilating-ideal graph of a commutative ring R is denoted by AG(R), whose vertices are all nonzero ideals of R with nonzero annihilators and two distinct vertices I and J are adjacent if and only if IJ - 0. In this paper, we consider the annihilating-ideal graphs of idealizations of commutative rings. We study the behavior of the girth and diameter of the annihilating-ideal graph of a commutative ring when extending to idealizations of the ring.
引用
收藏
页码：165 / 168
页数：4
相关论文
共 50 条
  • [41] PRIMARY DECOMPOSITION OF HOMOGENEOUS IDEAL IN IDEALIZATION OF A MODULE
    Tran Nguyen An
    STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2018, 55 (03) : 345 - 352
  • [42] A graph associated with the set of all nonzero annihilating ideals of a commutative ring
    Visweswaran, S.
    Patel, Hiren D.
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2014, 6 (04)
  • [43] The Co-annihilating-ideal Graphs of Commutative Rings
    Akbari, Saeeid
    Alilou, Abbas
    Amjadi, Jafar
    Sheikholeslami, Eyed Mahmoud
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2017, 60 (01): : 3 - 11
  • [44] On the strongly annihilating-submodule graph of a module
    Beyranvand, R.
    Farzi-Safarabadi, A.
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2022, 51 (02): : 443 - 454
  • [45] On the inclusion ideal graph of a poset
    Jahanbakhsh, N.
    Nikandish, R.
    Nikmehr, M. J.
    ALGEBRA AND DISCRETE MATHEMATICS, 2019, 27 (02): : 269 - 279
  • [46] On the complement of a graph associated with the set of all nonzero annihilating ideals of a commutative ring
    Visweswaran, S.
    Sarman, Patat
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2016, 8 (03)
  • [47] Maximal Ideal Graph of Commutative Semirings
    Alwan, Ahmed H.
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2021, 12 (01): : 913 - 926
  • [48] THE TOTAL GRAPH OF ANNIHILATING ONE-SIDED IDEALS OF A RING
    Alibemani, Abolfazl
    Hashemi, Ebrahim
    Alhevaz, Abdollah
    INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 2020, 27 : 61 - 76
  • [49] Comaximal graph of amalgamated algebras along an ideal
    Shoar, Hanieh
    Salimi, Maryam
    Tehranian, Abolfazl
    Rasouli, Hamid
    Tavasoli, Elham
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 22 (01)
  • [50] Prime ideal sum graph of a commutative ring
    Saha, Manideepa
    Das, Angsuman
    Celikel, Ece Yetkin
    Abdioglu, Cihat
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 22 (06)
12345