ON THE STRUCTURE OF A k-ANNIHILATING IDEAL HYPERGRAPH OF COMMUTATIVE RINGS

被引：1

作者：

Essa, Shaymaa S. ^{[1
]}

Mohammad, Husam Q. ^{[2
]}

机构：

[1] Duhok Univ, Dept Math, Duhok 42001, Kurdistan Regio, Iraq

[2] Univ Mosul, Dept Math, Mosul 41002, Iraq

来源：

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2023年 / 38卷 / 01期

关键词：

Subject Classification; Key words and phrases; Finite reduced ring; direct product of ideals; k-annihilating ideal hypergraph; and k-zero divisor hypergraph; DOMINATION; GRAPHS;

D O I：

10.4134/CKMS.c210427

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

. In this paper we obtain a new structure of a k-annihilating ideal hypergraph of a reduced ring R, by determine the order and size of a hypergraph AGk(R). Also we describe and count the degree of every nontrivial ideal of a ring R containing in vertex set A(R, k) of a hypergraph AGk(R). Furthermore, we prove the diameter of AGk(R) must be less than or equal to 2. Finally, we determine the minimal dominating set of a k-annihilating ideal hypergraph of a ring R.

引用

页码：55 / 67

页数：13

共 50 条

[31] On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative rings
Rehman, Nadeem ur
Mir, Shabir Ahmad
Nazim, Mohd
Nazim, Nazim
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2025, 19 (01):
[32] On the coloring of the annihilating-ideal graph of a commutative ring
Aalipour, G.
Akbari, S.
Nikandish, R.
Nikmehr, M. J.
Shaveisi, F.
DISCRETE MATHEMATICS, 2012, 312 (17) : 2620 - 2626
[33] On Annihilating Graphs Associated with Modules over Commutative Rings
Raja, Rameez
Pirzada, Shariefuddin
ALGEBRA COLLOQUIUM, 2022, 29 (02) : 281 - 296
[34] Ideal containment in commutative rings
Mimouni, Abdeslam
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 22 (09)
[35] 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
[36] A topological property of a hypergraph assigned to commutative rings
Selvakumar, K.
Jemi, J. Beautlin
Hamzekolaee, A. R. Moniri
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2025, 24 (03)
[37] The spectrum subgraph of the annihilating-ideal graph of a commutative ring
Taheri, R.
Behboodi, M.
Tehranian, A.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (08)
[38] On the clique number of the complement of the annihilating ideal graph of a commutative ring
Visweswaran S.
Patel H.D.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016, 57 (2): : 307 - 320
[39] 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)
[40] THE ANNIHILATING-SUBMODULE GRAPH OF MODULES OVER COMMUTATIVE RINGS
Ansari-Toroghy, Habibollah
Habibi, Shokoufeh
MATHEMATICAL REPORTS, 2018, 20 (03): : 245 - 262

← 1 2 3 4 5 →