Volume 69 | Issue 6 | Year 2023 | Article Id. IJMTT-V69I6P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I6P502
Received | Revised | Accepted | Published |
---|---|---|---|
10 Apr 2023 | 19 May 2023 | 04 Jun 2023 | 15 Jun 2023 |
In this paper, we define an annihilator (a: b) in a distributive q-lattice A, and we prove (a:b), which we call an annihilator of ‘a’ relative to ‘b’, is an ideal of A. Also, we observe some basic properties of these annihilators.
[1] Ivan Chajada, “Lattices in Quasiordered Sets,” Acta Universitatis Palackianae Olomucensis Facultas Rerum Naturalium. Mathematica, vol. 31, no. 1, pp. 6-12, 1992.
[Google Scholar] [Publisher Link]
[2] G.C. Rao et al., “Some Remarks on Distributive Q-Lattices,” International Journal of Computational Cognition, vol. 9, no. 2, pp. 79 -81, 2011.
[Google Scholar] [Publisher Link]
[3] G.C. Rao, and M. Sambasiva Rao, “Relative Annihilators in Almost Distributive Lattices,” International Journal of Computational Cognition, vol. 9, no. 2, 2011.
[4] A.D. Lokhande, and Ashok S. Kulkarni, “Filter and Annihilator in Distributive q-lattices,” Online International Interdisciplinary Research Journal [Bi-Monthly], vol. 3, no. 1, pp. 68-77, 2013.
[Publisher Link]
[5] G.C. Rao, and M. Sambasiva Rao, “Annihilators ideals in Almost Distributive Lattices,” International Mathematical Forum, vol. 4, no. 15, pp. 733-746, 2009.
[Google Scholar] [Publisher Link]
[6] G.C. Rao, and S. Ravi Kumar, “Minimal Prime Ideals in Almost Distributive Lattices,” International Journal of Contemporary Mathematical Sciences, vol. 4, no. 10, pp. 475-484, 2009.
[Google Scholar] [Publisher Link]
[7] A.D. Lokhande, and Ashok S. Kulkarni, “Some Remarks in Semi q-Lattices,” International Journal of Latest Research in Science and Technology, vol. 4, no. 6, pp. 12-14, 2015.
[Publisher Link]
[8] Ashok S. Kulkarni, and A.D. Lokhande, “Remarks on Ideal in Distributive Q-lattices,” Online International Interdisciplinary Research Journal [Bi-Monthly], vol. 3, pp. 54-63, 2013.
[Publisher Link]
[9] Manisha Vasantrao Patil, “Generalizations of Distributive Lattices,” Doctoral Thesis, Department of Mathematics, Shivaji University, Kolhapur, 2008.
[10] A.D. Lokhande, and Ashok S. Kulkarni, “Semi- Ideal and Semi-Filter in Distributive Q-lattices,” International Journal on Recent and Innovation Trends in Computing and Communication, vol. 2, no. 3, pp. 501-506, 2014.
[Google Scholar] [Publisher Link]
[11] A.S.A. Noor, and Momtaz Begum, “Some Properties of 0-distributive Meet Semilattices,” Annals of Pure and Applied Mathematics, vol. 2, no. 1, pp. 60-66, 2012.
[Google Scholar] [Publisher Link]
[12] H.S. Chakraborty, and M.R. Talukder, “Some Characterizations of 0-Distributive Semilattices,” Mathematics Subject Classification, 2012.
[Google Scholar] [Publisher Link]
[13] P. Balasubramani, “Characterizations of the 0-Distributive Semilattice,” Mathematica Bohemica, vol. 128, no. 3, pp. 237-252, 2003.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Y.S. Pawar, and A.D. Lokhande, “Normal Semilattices,” Indian Journal of Puremathematics, vol. 29, no. 12, 1998.
[15] Y.S. Pawar, and N.K. Thakare, “0-Distributive Semilattices,” Canadian Mathematical Bulletin, vol. 21, no. 4, pp. 469-475, 1978.
[CrossRef] [Google Scholar] [Publisher Link]
[16] Ashok S Kulkarni, and A.D. Lokhande, “Semi Prime Ideal in a-Distributive Lattice,” International Journal of Mathematics and Its Applications, vol. 6, no. 3, pp. 63-68, 2018.
[Google Scholar] [Publisher Link]
[17] Ashok S Kulkarni, “Atom and Semi Atom in A-Distributive Poset,” International Journal of Research and Analytical Reviews, vol. 6, no. 1, pp. 147-149.
[18] Aroon Dattatraya Lokhande, “A Study of Ideals In Lattices and Semilattices,” Doctoral Thesis, Department of Mathematics, Shivaji University, Kolhapur, 2000.
[19] C. Jayaram, “Semi-atoms in Semilattices,” Mathematics Seminar Notes, vol. 10, pp. 351-366, 1982.
Ashok S Kulkarni, "Annihilator in a Distributive q-Lattice," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 6, pp. 8-11, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I6P502