آمار
| تعداد نشریات | 6 |
| تعداد شماره‌ها | 129 |
| تعداد مقالات | 1,616 |
| تعداد مشاهده مقاله | 1,853,238 |
| تعداد دریافت فایل اصل مقاله | 1,715,884 |
On the (outer)planarity of the intersection graph of idealization | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 تیر 1405 اصل مقاله (405.56 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31194.2777 | ||
| نویسندگان | ||
| Nematollah Shirmohammadi* 1؛ Akram Mahmoodi2؛ Alireza Vahidi2 | ||
| 1Department of Pure Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran | ||
| 2Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity. The intersection graph of ideals of a ring $R$ is an undirected simple graph denoted by $\Gamma(R)$ whose vertices are in a one-to-one correspondence with nonzero proper ideals and two distinct vertices are joined by an edge if and only if the corresponding ideals of $R$ have a nonzero intersection. Let $M$ be a unitary nonzero $R$-module and let $R\ltimes M$ be the idealization of $M$ in $R$. In this paper, we provide a characterization of the planarity of the intersection graph of idealization. We then conclude that the intersection graph of idealization is planar if and only if it is outerplanar. | ||
| کلیدواژه‌ها | ||
| Idealization؛ intersection graph؛ planarity | ||
| مراجع | ||
|
[1] S. Akbari and R. Nikandish, Some results on the intersection graph of ideals of matrix algebras, Linear Multilinear Algebra 62 (2014), no. 2, 195–206. https://doi.org/10.1080/03081087.2013.769101
[2] S. Akbari, R. Nikandish, and M.J. Nikmehr, Some results on the intersection graphs of ideals of rings, J. Algebra Appl. 12 (2013), no. 4, 1250200. https://doi.org/10.1142/S0219498812502003
[3] D. Anderson and M.R. Winders, Idealization of a module, J. Commut. Algebra 1 (2009), no. 1, 3–56. https://doi.org/10.1216/JCA-2009-1-1-3
[4] D.F. Anderson and P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434–447. https://doi.org/10.1006/jabr.1998.7840 [5] M.F. Atiyah and I.G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, Boston, 1969.
[6] M. Axtell and J. Stickles, Zero-divisor graphs of idealizations, J. Pure Appl. Algebra 204 (2006), no. 2, 235–243. https://doi.org/10.1016/j.jpaa.2005.04.004 [7] C. Bakkari, S.E. Kabbaj, and N. Mahdou, Trivial extensions defined by prüfer conditions, J. Pure Appl. Algebra 214 (2010), no. 1, 53–60. https://doi.org/10.1016/j.jpaa.2009.04.011
[8] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208–226. https://doi.org/10.1016/0021-8693(88)90202-5
[9] N. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl. 10 (2011), no. 4, 727–739. https://doi.org/10.1142/S0219498811004896
[10] I. Chakrabarty, S. Ghosh, T.K. Mukherjee, and M.K. Sen, Intersection graphs of ideals of rings, Discrete Math. 309 (2009), no. 17, 5381–5392. https://doi.org/10.1016/j.disc.2008.11.034
[11] J.A. Huckaba, Commutative Rings with Zero Divisors, M. Dekker, New York, 1988.
[12] A. Mahmoodi, A. Vahidi, R. Manaviyat, and R. Alipour, Intersection graph of idealizations, Collect. Math. 75 (2024), no. 3, 693–702. https://doi.org/10.1007/s13348-023-00407-7
[13] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999.
[14] M. Nagata, Local Rings, Interscience, New York, 1962.
[15] D.B. West, Introduction to Graph Theory, second ed., Prentice Hall, 2001. | ||
|
آمار تعداد مشاهده مقاله: 103 تعداد دریافت فایل اصل مقاله: 131 |
||