An ideal-based cozero-divisor graph of a commutative ring
Résumé
Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this article, we introduce the cozero-divisor graph $\acute{\Gamma}_I(R)$ of $R$ and explore some of its basic properties. This graph can be regarded as a dual notion of an ideal-based zero-divisor graph.
Téléchargements
Références
M. Afkhami and K. Khashyarmanesh, The cozero-divisor graph of a commutative ring, Southeast Asian Bull. Math. 35, 753-762, (2011).
M. Afkhami and K. Khashyarmanesh, On the cozero-divisor graphs of commutative rings and their complements, Bull. Malays. Math. Sci. Soc. 35, 935-944, (2012).
M. Afkhami and K. Khashyarmanesh, On the cozero-divisor graphs of commutative rings, Appl. Math. 4, 979-985, (2013). https://doi.org/10.4236/am.2013.47135
D. F. Anderson, Sh. Ghalandarzadeh, S. Shirinkam, and P. Malakooti Rad, On the diameter of the graph ΓAnn(M) (R), Filomat 26 (3), 623-629, (2012). https://doi.org/10.2298/FIL1203623A
D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217, 434-447, (1999). https://doi.org/10.1006/jabr.1998.7840
D .F. Anderson and S. Shirinkam, Some remarks on the graph ΓI (R), Comm. Algebra 42, 545-562, (2014). https://doi.org/10.1080/00927872.2012.718021
H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math. 11 (4), 1189-1201, (2007). https://doi.org/10.11650/twjm/1500404812
H. Ansari-Toroghy and F. Farshadifar, The dual notion of some generalizations of prime submodules, Comm. Algebra 39, 2396-2416, (2011). https://doi.org/10.1080/00927872.2010.488684
J. A. Bondy and U. S. R. Murty, Graph theory with applications, American Elsevier, New York, 1976. https://doi.org/10.1007/978-1-349-03521-2
S. Ebrahimi Atani and A. Yousefian Darani, Zero-divisor graphs with respect to primal and weakly primal ideals, J. Korean Math. Soc. 46, 313-325, (2009). https://doi.org/10.4134/JKMS.2009.46.2.313
P. Dheena and B. Elavarasan, An ideal-based zero-divisor graph of 2-primal near-rings, Bull. Korean Math. Soc. 46, 1051-1060, (2009). https://doi.org/10.4134/BKMS.2009.46.6.1051
L. Fuchs, On primal ideals, Proc. Amer. Math. Soc. 1, 1-6, (1950). https://doi.org/10.1090/S0002-9939-1950-0032584-8
I. Kaplansky, Commutative rings, University of Chicago, (1978).
M. J. Nikmehr and S. Khojasteh, A generalized ideal-based zero-divisor graph, J. Algebra Appl. 14 (6), 1550079, (2015). https://doi.org/10.1142/S0219498815500796
H. R. Maimani, M. R. Pournaki, and S. Yassemi, Zero-divisor graph with respect to an ideal, Comm. Algebra 34 (3), 923-929, (2006). https://doi.org/10.1080/00927870500441858
S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31, 4425-4443, (2003). https://doi.org/10.1081/AGB-120022801
A. Yousefian Darani, Notes on the ideal-based zero-divisor graph, J. Math. Appl. 32, 103-107, (2010).
Copyright (c) 2021 Boletim da Sociedade Paranaense de Matemática

Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).