Some results on the maximal graph of commutative rings

被引：1
|
作者：
Soleimani, M. [1 ]
Mahmudi, F. [1 ]
Naderi, M. H. [1 ]
机构：
[1] Univ Qom, Fac Sci, Dept Math, Qom 8731751167, Iran
来源：
ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL | 2023年 / 16卷
关键词：
commutative rings; energy of a graph; maximal graph; nonseparable graph;
D O I：
10.32513/asetmj/1932200823104
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let (Gamma(R))(c) be the maximal graph of a commutative ring with identity R whose vertices are elements of R. Two distinct vertices a and b are adjacent if and only if Ra + Rb not equal R or there exists a maximal ideal of R containing both them. In this paper, we study some properties of two (induced) subgraphs (Gamma 2(R))(c) and (G(R))(c) of (Gamma(R))(c).
引用
收藏
页码：21 / 26
页数：6
相关论文
共 50 条
  • [41] On the existence of maximal subrings in commutative noetherian rings
    Azarang, A.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (01)
  • [42] Commutative rings with infinitely many maximal subrings
    Azarang, Alborz
    Oman, Greg
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2014, 13 (07)
  • [43] Most Commutative Rings Have Maximal Subrings
    Azarang, A.
    Karainzadeh, O. A. S.
    ALGEBRA COLLOQUIUM, 2012, 19 : 1139 - 1154
  • [44] Thek-maximal hypergraph of commutative rings
    Selvakumar, K.
    Amritha, V. C.
    BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, 2020, 61 (04): : 747 - 757
  • [45] On commutative rings whose maximal ideals are idempotent
    Kourki, Farid
    Tribak, Rachid
    COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2019, 60 (03): : 313 - 322
  • [46] The k-maximal hypergraph of commutative rings
    K. Selvakumar
    V. C. Amritha
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2020, 61 : 747 - 757
  • [47] ON THE EXISTENCE OF MAXIMAL SUBRINGS IN COMMUTATIVE ARTINIAN RINGS
    Azarang, A.
    Karamzadeh, O. A. S.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2010, 9 (05) : 771 - 778
  • [48] Some further results on the annihilator ideal graph of a commutative ring
    1600, Politechnica University of Bucharest (79):
  • [49] PERFECT CODES IN INDUCED SUBGRAPH OF UNIT GRAPH ASSOCIATED WITH SOME COMMUTATIVE RINGS
    Mudaber, Mohammad Hassan
    Sarmin, Nor Haniza
    Gambo, Ibrahim
    JURNAL TEKNOLOGI-SCIENCES & ENGINEERING, 2022, 84 (05): : 131 - 136
  • [50] Some results on the complement of the annihilating ideal graph of a commutative ring
    Visweswaran, S.
    Patel, Hiren D.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (07)
12345