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Zero Divisor Graph of a Poset with Respect to Primal Ideals
Authors: Hossein Pourali
Abstract:In this paper, we extend the concepts of primal and weakly primal ideals for posets. Further, the diameter of the zero divisor graph of a poset with respect to a non-primal ideal is determined. The relation between primary and primal ideals in posets is also studied.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1131756Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 880
 D. F. Anderson and J. D. LaGrange, Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph, J. Pure Appl. Algebra, 216 (2012), 1626-1636.
 S. E. Attani, On primal and wekly primal ideals over commutative semirings, Glasnik Matematicki, 43, (2008), 13-23.
 S. E. Attani and A. Y. Darani, Zero divisor graphs with respect to primal and weakly primal ideas, J. Korean Math. Soc. 46 (2009), 313-325.
 I. Beck, Coloring of a Commutative Ring, J. Algebra 116 (1988), 208- 226 .
 F. R. DeMeyer, T. McKenzie and K. Schneider, The Zero-Divisor Graph of a Commutative Semigroup, Semigroup Forum 65 (2002), 206-214.
 R. Halaˇs, Ideals and annihilators in ordered sets, Czech. Math . J. 45 (1995), 127-134.
 R. Halaˇs and H. L¨anger, The zero divisor graph of a qoset, Order 27, 343-351.
 R. Halaˇs and M. Jukl, On Beck’s coloring of posets, Discrete Math. 309 (2009), 4584-4589.
 V. V. Joshi, Zero divisor graph of a poset with respect to an ideal, Order 29 (2012), 499-506.
 V. V. Joshi and Nilesh Mundlik , On primary ideals in poset, Mathematica Slovaca 65 (2016),1237-1250 .
 V. V. Joshi, B. N. Waphare, and H. Y. Pourali, Zero divisor graphs of lattices and primal ideals, Asian-Eur. J. Math. 5 (2012), 1250037- 1250046.
 V. V. Joshi , B. N. Waphare and H. Y. Pourali, Generalized zero divisor graph of a poset, Discrete Appl. Math. 161 (2013),1490-1495.
 V. V. Joshi, B. N. Waphare, and H. Y. Pourali, The graph of equivalence classes of zero divisors, ISRN Discrete Math. (2014). Article ID 896270, 7 pages. http:// dx.doi.org/101155/2014/896270.
 H. Y. Pourali, V. V. Joshi and B. N. Waphare, Diameter of zero divisor graphs of finite direct product of lattices, World Academy of Science, Engineering and Technology. (2014). Vol: 8, No:9.
 D. Lu and T. Wu, The zeor divisor graphs of posets and an application to semigroups, 26 (2010), 793-804.
 S. K. Nimbhorkar , M. P. Wasadikar and Lisa DeMeyer, Coloring of semilattices, Ars Comb. 12 (2007), 97-104 .
 S.P. Redmond, The zero-divisor graph of a non-commutative ring, Int. J. Comm. Rings 4 (2002), 203-211.
 P. V. Venkatanarsimhan, Semi-ideals in posets, Math. Annalen 185 (1970), 338-348.
 D. B. West, Introduction to Graph Theory, Practice Hall, New Delhi, 2009.