Intersection graph of amalgamated algebras along an ideal

Salimi, Maryam; Nafarieh Talkhooncheh, Elahe; Rasouli, Hamid; Tavasoli, Elham; Tehranian, Abolfazl

doi:10.22098/jhs.2026.18163.1127

دانشگاه محقق اردبیلی

تعداد نشریات	31
تعداد شماره‌ها	484
تعداد مقالات	4,286
تعداد مشاهده مقاله	7,298,689
تعداد دریافت فایل اصل مقاله	4,896,196

	Intersection graph of amalgamated algebras along an ideal
Journal of Hyperstructures
دوره 15، شماره 1، شهریور 2026، صفحه 24-33 اصل مقاله (1.62 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22098/jhs.2026.18163.1127
نویسندگان
Maryam Salimi^* ¹؛ Elahe Nafarieh Talkhooncheh²؛ Hamid Rasouli²؛ Elham Tavasoli¹؛ Abolfazl Tehranian²
¹Department of Mathematics, ET.C., Islamic Azad University, Tehran, Iran
²Department of Mathematics, SR.C., Islamic Azad University, Tehran, Iran
چکیده
Let f:R→S be a ring homomorphism of commutative rings with identity, and let J be a non-zero proper ideal of S. The amalgamation of R with S along J with respect to f denoted by R∝^fJ, was introduced by D'Anna et al. in 2010. In this paper, we investigate some properties of the intersection graph of ideals of R∝^fJ. We show that Γ(R∝^fJ) is always connected and diam(Γ(R∝^fJ))≤2. We obtain some conditions which implies that for an integer n >0, K_{n} is a subgraph of Γ(R∝^fJ). We show that if R is a local ring, and J⊆Jac(S), where Jac(S) is the Jacobson radical of S, then Γ(R∝^fJ) is planar if and only if Γ(R∝^fJ) is star graph or K₃ or K₄, provided under certain conditions. Finally, we study the dominating number of Γ(R∝^fJ).
کلیدواژه‌ها
Amalgamation؛ complete graph؛ intersection graph؛ reduced ring

مراجع
[1] S. Akbari and R. Nikandish,Some results on the intersection graph of ideals of matrix algebras, Linear and Multilinear Algebra, 62 (2014), 195–206. [2] S. Akbari, R. Nikandish and M.J. Nikmehr, Some results on the intersection graphs of ideals of rings, Journal of Algebra and its Applications, 12 (2013), 13 pages. [3] Y. Azimi, The diameter of the zero-divisor graph of an amalgamated algebra, Collectanea Mathematica, 70 (2019), 399–405. [4] J. Bosak, The graphs of semigroups, Theory of Graphs and Application (M. Fielder, ed.), Academic Press, New York, 1964. [5] I. Chakrabarty, S. Ghosh, T.K. Mukherjee and M. K. Sen, Intersection graphs of ideals of rings, Discrete Mathematics, 309 (2009), 5381–5392. [6] M. Chhiti and N. Mahdou, Homological dimensions of the amalgamated duplication of a ring along a pure ideal, African Diaspora Journal of Mathematics, 10 (2010), 1–6. [7] M. Chhiti and N. Mahdou, Some homological dimensions of the amalgamated duplication of a ring along an ideal, Bulletin of Iranian Mathematical Society, 38 (2012), 507–515. [8] M. Chhiti, N. Mahdou and M. Tamekkante, Clean property in amalgamated algebras along an ideal, Hacettepe Journal of Mathematics and Statistics, 44 (2015), 41–49. [9] P. Chen, A kind of graph structure of rings, Algebra Colloquium, 10 (2003), 229–238. [10] B. Cs´ak´any and G. Poll´ak, The graph of subgroups of a finite group, Czechoslovak Mathematical Journal, 19 (1969), 241–247. [11] M. D’Anna, A construction of Gorenstein rings, Journal of Algebra, 306 (2006), 507–519. [12] M. D’Anna, C. A. Finocchiaro and M. Fontana, Amalgamated algebras along an ideal, in “Commutative Algebra and Applications”, Proccedings of the Fifth International Fez Conference on Commutative Algebra and Applications , Fez, Morocco, 2008, W. de. Gruyter Publisher, Berlin, 2009. [13] M. D’Anna, C. A. Finocchiaro and M. Fontana, New algebraic properties of an amalgamated algebra along an ideal, Communications in Algebra, 44 (2016), 1836–1851. [14] M. D’Anna, C. A. Finocchiaro and M. Fontana, Properties of chains of prime ideals in an amalgamated algebra along an ideal, Journal of Pure and Applied Algebra, 214 (2010), 1633–1641. [15] M. D’Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, Journal of Algebra and Its applications, 6 (2007), 443–459. [16] M. D’Anna and M. Fontana, The amalgamated duplication of a ring along a multiplicative-cannonical ideal, Arkiv f¨or Matematik, 45 (2007), 241–252. [17] R. Diestel, Graph Theory, Second ed., Graduate Texts in Mathematics, 173, Springer-Verlag, New York, 2000. [18] R.P. Grimaldi, Graphs from rings, Congressus Numerantium, 71 (1990), 95–103. [19] S.H. Jafari and N. J. Rad, Domination in the intersection graphs of rings and modules, Italian Journal of Pure and Applied Mathematics, 28 (2011), 17–20. [20] S. H. Jafari and N. J. Rad, Planarity of intersection graphs of ideals of rings, Internatinal Electronic Journal of Algebra, 8 (2010), 161–166. [21] N. Mahdou, A. Mimouni and M.A.S. Moutui, On pm-rings, rings of finite character and h-local ring, Journal of Algebra and Its applications, 13 (2014), 11 pages. [22] N. Mahdou, S. Moussaoui and S. Yassemi, The divided, going-down, and Gaussian properties of amalgamation of rings, Communications in Algebra, 49 (2021), 1938–1949. [23] N. Mahdou and M. Tamekkante, Gorenstein global dimension of an amalgamated duplication of a coherent ring of along an ideal, Mediterranean Journal of Mathematics, 8 (2011), 293–305. [24] H. R. Maimani and S. Yassemi, Zero-divisor graphs of amalgamated duplication of a ring along an ideal, Journal of Pure an Applied Algebra, 212 (2008), 168–174. [25] J. Shapiro, On a construction of Gorenstein rings proposed by M.D’Anna, Journal of Algebra, 323 (2010), 1155–1158. [26] H. Shoar, M. Salimi, A. Tehranian, H. Rasouli and E. Tavasoli, Comaximal graph of amalgamated algebras along an ideal, Journal of Algebra and its applications, 22 (2023), 11 pages. [27] E. Tavasoli, Some homological properties of amalgamation, Matematicki Vesnik, 68 (2016), 254–258.
آمار تعداد مشاهده مقاله: 126 تعداد دریافت فایل اصل مقاله: 81

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Intersection graph of amalgamated algebras along an ideal