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A note on total graph of commutative krasner hyperrings | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 1، مهر 2025، صفحه 87-97 اصل مقاله (169.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.24911.1553 | ||
| نویسندگان | ||
| E. Navidinia1؛ A. khojali* 2؛ F. Esmaeili Khalil Saraei3 | ||
| 1Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran | ||
| 2Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran | ||
| 3Fouman Faculty of Engineering, College of Engineering, University of Tehran, Fouman, Iran | ||
| چکیده | ||
| The purpose of this paper is to introduce the notion of total graph of Krasner hyperrings. In this regard, a connection between the graph theory and the theory of hyperrings is constructed and some fundamental properties of the total graph of Krasner hyperrings are investigated. Finally, for a multiplicative-prime subset $H$ of a hyperring $R$, the diameter and the girth of $\Gamma_{\!\!H}(R\setminus H)\,\mbox{and}\, \Gamma_{\!\!H}(H)$ are computed precisely. | ||
| کلیدواژه‌ها | ||
| Total graph؛ Krasner hyperring؛ Prime hyperideal | ||
| مراجع | ||
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[1] R. Ameri, M. Hamidi and H. Mohammadi, Hyperideals of (finite) general hyperrings, Mathematics Interdisciplinary Research, (4) 6 (2021), 257-273. [2] D. F. Anderson, T. Asir, A. Badawi and T. T. Chelvam, Graphs from Rings, New York, NY, USA: Springer International Publishing, 2021. [3] D. F. Anderson and A. Badawi, The generalized total graph of a commutative ring, Journal of Algebra and Its Applications, (5) 12 (2013), 1250212. [4] A. Asokkumar, Derivations in hyperrrings and prime hyperrings, Iranian Journal of Mathematical Sciences and Informatics, (1) 8 (2013), 1-13. [5] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007. [6] F. Esmaeili Khalil Saraei, H. Heydarinejad Astaneh and R. Navidinia, The total graph of a module with respect to multiplicative-prime subsets, Rom. J. Math. Comput. Sci, (2) 4 (2014), 151-166. [7] F. Esmaeili Khalil Saraei and E. Navidinia, On the extended total graph of modules over commutativerings, International Electronic Journal of Algebra, 25 (2019), 77-86. [8] F. Esmaeili Khalil Saraei and E. Navidinia, A note on the extended total graph of commutative rings, Journal of Algebra and Related Topics, (1) 6 (2018), 25-33. [9] M. Hamidi, R. Ameri and H. Mohammadi, Hyperideal-based intersection graphs, Indian J. Pure Appl Math, (1) 54 (2022), 120-132. [10] L. Kamali Ardekani and B. Davvaz, A generalization of prime hyperideals in Krasner hyperrings, Journal of Algebraic Systems, (2) 7 (2020), 205-216. [11] M. Krasner, Approximation des corps values complets de caracteristique p, p > 0, par ceux de caracteristique zero, Colloque d′ Algebre Superieure (Bruxelles, Decembre 1956), CBRM, Bruxelles, (1957). [12] F. Marty, Sur une generalization de la notion de groupe, 8th Congres Math. Scandinaves, Stockholm, Sweden (1934), 45-49. | ||
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