پیوندهای مفید
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 852 |
| تعداد مقالات | 8,256 |
| تعداد مشاهده مقاله | 52,579,056 |
| تعداد دریافت فایل اصل مقاله | 9,089,782 |
Join maximal element graph of lattice modules | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 115-123 اصل مقاله (165.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.28291.1704 | ||
| نویسندگان | ||
| L. Sherpa1؛ V. Kharat1؛ M. Agalave2؛ N. M. Phadatare* 3 | ||
| 1Department of Mathematics, Savitribai Phule Pune University, Pune, India | ||
| 2Department of Mathematics, Fergusson College(Autonomus), Pune, India | ||
| 3Bharati Vidyapeeth Deemed to be University College of Engineering, Pune, India | ||
| چکیده | ||
| Let $\pounds$ be a $C$-lattice and $M$ be a lattice module over $\pounds$. The join maximal element graph $\mathbb{G}(M)$ is a simple, undirected graph with all proper non-zero elements of $M$ as vertices, and two distinct vertices, $N$ and $K$, are adjacent if and only if $N\vee K\in Max(M)$, where $Max(M)$ is the collection of all maximal elements of $M$. In this paper, some properties of the graph $\mathbb{G}(M)$ like diameter, girth and clique number are investigated. Also, the interplay between the algebraic properties of $M$ and the properties of those graphs is studied. | ||
| کلیدواژهها | ||
| Maximal element؛ Jacobson radical $J_{rad}(M)$؛ Join maximal element graph $\mathbb{G}(M)$ | ||
| مراجع | ||
|
[1] A. Abbasi and Sh. Habibi, The total graph of a module over a commutative ring with respect to proper submodules, J. Algebra Appl., (3) 11 (2012), 1250048. [2] E. A. AL-Khouja, Maximal elements and prime elements in lattice modules, Damascus Univ. Basic Sci., 19 (2003), 9-20. [3] S. Akbari, H. A. Tavallaee, and S. Khalashi Ghezelahmad, Intersection graph of submodules of a module, J. Algebra Appl., (1) 11 (2012), 1250019. [4] F. H. Abdulqadr, Maximal ideal graph of commutative rings, Iraqi J. Sci., (8) 61 (2020), 2070-2076. [5] A. H. Alwan, Maximal submodule graph of a module, J. Discrete Math. Sci. Cryptogr., (7) 24 (2021), 1941-1949. [6] S. Akbari and A. Mohammadian, On the zero-divisor graph of a commutative ring, J. Algebra, (2) 274 (2004), 847-855. [7] D. F. Anderson, R. Levy and J. Shapiro, Zero-divisor graphs, von Neumann regular rings and Boolean algebras, J. Pure Appl. Algebra, 180 (2003), 221-241. [8] F. F. Anderson and M. Naseer, Beck’s coloring of a commutative ring, J. Algebra, 159 (1993), 500-514. [9] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, (2) 217 (1999), 434-447. [10] H. Ansari-Toroghy and Sh. Habibi, The zariski topology-graph of modules over commutative rings, Commun. Algebra, 42 (2014), 3283-3296. [11] H. Ansari-Toroghy, F. Farshadifar and F. Mahboobi-Abkenar, The small intersection graph relative to multiplication modules, J. Algebra Relat. Topics, (1) 4 (2016), 21-32. [12] I. Beck, Coloring of commutative rings, J. Algebra, 116 (1988), 208-226. [13] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings-I, J. Algebra Appl., (4) 10 (2011), 727-739. [14] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings-II, J. Algebra Appl., (4) 10 (2011), 741-753. [15] J. Bondy and U. Murty, Graph Theory, Graduate Texts in Mathematics 244, Springer, New York, 2008. [16] F. Callialp, G. Ulucak and U.Tekir, On the Zariski topology over an L-module M, Turk. J. Math., 41 (2017), 326-336. [17] F. Callialp, C. Jayaram and U.Tekir, Weakly prime elements in multiplicative lattices, Commun. Algebra, 40 (2012), 2825-2840. [18] J. A. Johnson, a-Adic completions of Noetherian lattice modules, Fund. Math., 66 (1970), 341-371. [19] C. Jayaram and E. W. Johnson, s-Prime elements in multiplicative lattices, Period. Math. Hung., 31 (1995), 201-208. [20] F. Harary, Graph Theory, Narosa, New Delhi, 1988. [21] H. M. Nakkar, E. A. AL-Khouja and GH. Al-Mohammad, A characterization of regular lattice modules by the radical elements, 40th-science week at the University of Tachreen, 2 (2000), 63-75. [22] N. Phadatare, V. Kharat and S. Ballal, Semi-complement graph of lattice modules, Soft Computing, 23 (2019), 3973-3978. [23] S. Rajaee, Essential submodules relative to a submodule, J. Algebra Relat. Topics, (2) 11 (2023), 59-71. [24] D. B. West, Introduction to graph theory, Second ed., Prentice-Hall of India, New Delhi, 2002. | ||
|
آمار تعداد مشاهده مقاله: 49 تعداد دریافت فایل اصل مقاله: 71 |
||