Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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zJ-Ideals and Strongly Prime Ideals in Posets

  • Received : 2015.05.26
  • Accepted : 2017.05.17
  • Published : 2017.10.23
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Abstract

In this paper, we study the notion of $z^J$ - ideals of posets and explore the various properties of $z^J$-ideals in posets. The relations between topological space on Sspec(P), the set $I_Q=\{x{\in}P:L(x,y){\subseteq}I\text{ for some }y{\in}P{\backslash}Q\}$ for an ideal I and a strongly prime ideal Q of P and $z^J$-ideals are discussed in poset P.

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References

  1. F. Azarpanah, A. S Karamzadeh and A.Rezai Aliabad, On Ideals Consisting Entirely of Zero Divisor, Comm. Algebra, 28(2)(2000), 1061-1073. https://doi.org/10.1080/00927870008826878
  2. J. Catherine Grace John and B. Elavarasan, Strongly Prime and Strongly Semiprime ideals in Posets, Global Journal of Pure and Applied Mathematics, 11(5)(2015), 2965-2970.
  3. J. Catherine Grace John and B. Elavarasan, Primeness of extension of semi-ideals in posets, Applied Mathematical Sciences, 164(8)(2014), 8227-8232.
  4. B. Elavarasan and K. Porselvi, An ideal-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
  5. R. Halas, On extension of ideals in posets, Discrete Mathematics, 308(2008), 4972-4977. https://doi.org/10.1016/j.disc.2007.09.022
  6. V. S. Kharat and K. A. Mokbel, Primeness and semiprimeness in posets, Math. Bohem., 134(1)(2009), 19-30.
  7. G. Mason, z-ideals and prime ideals, J. Algebra, 26(1973), 280-297. https://doi.org/10.1016/0021-8693(73)90024-0
  8. P. V. Venkatanarasimhan, Semi ideals in posets, Math. Ann., 185(4)(1970), 338-348. https://doi.org/10.1007/BF01349957