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Poset Properties Determined by the Ideal - Based Zero-divisor Graph

  • Porselvi, Kasi (Department of Mathematics, School of Science and Humanities, Karunya University) ;
  • Elavarasan, Balasubramanian (Department of Mathematics, School of Science and Humanities, Karunya University)
  • Received : 2011.11.29
  • Accepted : 2013.05.24
  • Published : 2014.06.23

Abstract

In this paper, we study some properties of finite or infinite poset P determined by properties of the ideal based zero-divisor graph properties $G_J(P)$, for an ideal J of P.

Keywords

References

  1. D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217(1999), 434-447. https://doi.org/10.1006/jabr.1998.7840
  2. I. Beck, Coloring of commutative rings, J. Algebra, 116(1988), 208-226. https://doi.org/10.1016/0021-8693(88)90202-5
  3. J. A. Bondy and U. S. R. Murty, Graph theory with applications, North-Holland, Amsterdam, 1976.
  4. F. R. DeMeyer, T. McKenzie and K. Schneider, The zero-divisor graph of a commutative semigroups, Semigroup Forum, 65(2002), 206-214. https://doi.org/10.1007/s002330010128
  5. P. Dheena and B. Elavarasan, An ideal based-zero-divisor graph of 2-primal near-rings, Bull. Korean Math. Soc., 46(6)(2009), 1051-1060. https://doi.org/10.4134/BKMS.2009.46.6.1051
  6. B. Elavarasan and K. Porselvi, An ldeal - based zero-divisor graph of posets, Commun. Korean Math. Soc., 28(1)(2013), 79-85. https://doi.org/10.4134/CKMS.2013.28.1.079
  7. H. R. Maimani, Median and Center of Zero-Divisor Graph of Commutative Semi-groups, Iran. J. Math. Sci. Inform., 3(2)(2008), 69-76.
  8. Radomr Hala and Marek Jukl, On beck's coloring of posets, Discrete Mathematics, 309(2009), 4584-4589. https://doi.org/10.1016/j.disc.2009.02.024
  9. Radomr Hala, On extensions of ideals in posets, Discrete Mathematics, 308(2008), 4972-4977. https://doi.org/10.1016/j.disc.2007.09.022
  10. S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra, 31(9)(2003), 4425-4443. https://doi.org/10.1081/AGB-120022801
  11. Tongsuo Wu and Dancheng Lu, Sub-semigroups determined by the zero-divisor graph, Discrete Mathematics, 308(2008), 5122-5135. https://doi.org/10.1016/j.disc.2007.09.032