On Non-Comaximal Graphs of Ideals of Commutative Rings
DOI:
https://doi.org/10.52737/18291163-2023.15.2-1-8Keywords:
Artinian Ring, Non-Comaximal Graph, Minimal IdealAbstract
In this paper, we relate some properties of non-comaximal graph of ideals of a commutative ring with identity with the properties of the ring.
References
D.F. Anderson and A. Badawi, The total graph of a commutative ring. J. Algebra, 320 (2008), no. 7, pp. 2706-2719. https://doi.org/10.1016/j.jalgebra.2008.06.028
B. Barman and K.K. Rajkhowa, Non-comaximal graph of ideals of a ring. Proc. Indian Acad. Sci. (Math. Sci.), 129 (2019), Article 76. https://doi.org/10.1007/s12044-019-0504-x
I. Beck, Coloring of commutative rings. J. Algebra, 116 (1988), no. 1, pp. 208-226. https://doi.org/10.1016/0021-8693(88)90202-5
I. Chakrabarty, S. Ghosh, T.K. Mukherjee, and M.K. Sen, Intersection graphs of ideals of rings. Discrete Math., 309 (2009), no. 17, pp. 5381-5392. https://doi.org/10.1016/j.disc.2008.11.034
F. Harary, Graph theory, Addison-Wesley Publishing Company, Reading, Mass., 1969.
T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds), Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
J.A. Huckaba, Commutative rings with zero-divisors, Marcel-Dekker, New York, Basel, 1988.
I. Kaplansky, Commutative rings, University of Chicago Press, Chicago, 1974.
F. Kasch, Modules and rings, Academic Press, London, 1982.
T. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, 189, Springer, New York, 1999.
J. Lambeck, Lectures on rings and modules, Blaisdell Publishing Company, Waltham, Toronto, London, 1966.
L.A. Mahdavi and Y. Talebi, Co-intersection graph of submodules of a module, Algebra Discrete Math., 21 (2016), no. 1, pp. 128-143.
P.K. Sharma and S.M. Bhatwadekar, A note on graphical representation of rings, J. Algebra, 176 (1995), no. 1, pp. 124-127. https://doi.org/10.1006/jabr.1995.1236
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