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http://dx.doi.org/10.5666/KMJ.2017.57.3.385

zJ-Ideals and Strongly Prime Ideals in Posets  

John, Catherine Grace (Department of Mathematics, Karunya University)
Elavarasan, Balasubramanian (Department of Mathematics, Karunya University)
Publication Information
Kyungpook Mathematical Journal / v.57, no.3, 2017 , pp. 385-391 More about this Journal
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.
Keywords
Poset; ideals; strongly prime ideal; minimal prime ideal; Zariski topology;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 F. Azarpanah, A. S Karamzadeh and A.Rezai Aliabad, On Ideals Consisting Entirely of Zero Divisor, Comm. Algebra, 28(2)(2000), 1061-1073.   DOI
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.   DOI
5 R. Halas, On extension of ideals in posets, Discrete Mathematics, 308(2008), 4972-4977.   DOI
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.   DOI
8 P. V. Venkatanarasimhan, Semi ideals in posets, Math. Ann., 185(4)(1970), 338-348.   DOI