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

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	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.
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Intersection graph of amalgamated algebras along an ideal