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Some results on a supergraph of the comaximal ideal graph of a commutative ring | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 3، شماره 2، اسفند 2018، صفحه 151-172 اصل مقاله (454.27 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2018.26132.1079 | ||
| نویسندگان | ||
| S. Visweswaran* 1؛ Jaydeep Parejiya2 | ||
| 1Saurashtra University | ||
| 2Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India. | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity such that $R$ admits at least two maximal ideals. In this article, we associate a graph with $R$ whose vertex set is the set of all proper ideals $I$ of $R$ such that $I$ is not contained in the Jacobson radical of $R$ and distinct vertices $I$ and $J$ are joined by an edge if and only if $I$ and $J$ are not comparable under the inclusion relation. The aim of this article is to study the interplay between the graph-theoretic properties of this graph and the ring-theoretic properties of the ring $R$. | ||
| کلیدواژهها | ||
| Chained ring؛ Bipartite graph؛ Split graph؛ Complemented graph | ||
| مراجع | ||
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[1] M. Afkhami and K. Khashyarmanesh, The cozero-divisor graph of a commutative ring., Southeast Asian Bull. Math. 35 (2011), no. 5, 753–762.
[2] M. Afkhami and K. Khashyarmanesh, On the cozero-divisor graphs and comaximal graphs of commutative rings, J. Algebra Appl. 12 (2013), no. 3, Article ID: 1250173, 9 pages.
[3] M. Afkhami and K. Khashyarmanesh, On the cozero-divisor graphs of commutative rings, Applied Mathematics 4 (2013), no. 7, 979–985.
[4] D.F. Anderson, R. Levy, and J. Shapiro, Zero-divisor graphs, von neumann regular rings, and boolean algebras, J. Pure Appl. Algebra 180 (2003), no. 3, 221–241.
[5] M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, AddisonWesley Publishing Company, Reading Massachusetts, 1969.
[6] R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, Universitext Springer, 2000.
[7] E. Bastida and R. Gilmer, Overrings and divisorial ideals of rings of the form D + M., Michigan Math. J. 20 (1973), no. 1, 79–95.
[8] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl. 10 (2011), no. 4, 727–739.
[9] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings II, J. Algebra Appl. 10 (2011), no. 4, 741–753.
[10] S.M. Bhatwadekar and P.K. Sharma, A note on graphical representation of rings, J. Algebra 176 (1995), no. 1, 124–127.
[11] R. Gilmer, Multiplicative Ideal Theory, Marcel-Dekker, New York, 1972.
[12] M.I. Jinnah and S.C. Mathew, When is the comaximal graph split?, Comm. Algebra 40 (2012), no. 7, 2400–2404.
[13] H.R. Maimani, M. Salimi, A. Sattari, and S. Yassemi, Comaximal graph of commutative rings, J. Algebra 319 (2008), no. 4, 1801–1808.
[14] S.M. Moconja and Z.Z. Petrovi´c, On the structure of comaximal graphs of commutative rings with identity, Bull. Aust. Math. Soc. 83 (2011), no. 1, 11–21.
[15] K. Samei, On the comaximal graph of a commutative ring, Canad. Math. Bull. 57 (2014), no. 2, 413–423.
[16] H.-Ju Wang, Graphs associated to co-maximal ideals of commutative rings, J. Algebra 320 (2008), no. 7, 2917–2933.
[17] M. Ye and T. Wu, Co-maximal ideal graphs of commutative rings, J. Algebra Appl. 11 (2012), no. 6, Article ID: 1250114, 14 pages. | ||
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