Normal Filters in Almost Distributive Lattices
Abstract
In this paper we introduce normal lters and normlets in an almostdistributive lattice with dense elements and reinforce them in both algebraical and topological aspects.
References
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[2] G. C. Rao and G. Nanaji Rao, Dense elements in almost distributive lattices, Southeast Asian Bull. Math., 27(6)(2004), 1081-1088.
[3] G. C. Rao and M. Sambasiva Rao, Annihilator ideal in almost distributive lattices, Int. Math. Forum., 4915)(2009), 733-746.
[4] G. C. Rao and M. Sambasiva Rao, Annulets in almost distributive lattices, Eur. J. Pure Appl. Math., 2(1)(2009), 58-72.
[5] G. C. Rao and S. Ravi Kumar, Minimal prime ideal in almost distributive lattices, Int. J. Contemp. Math. Sci., 4(10)(2009), 475-484.
[6] G. C. Rao, G. Nanaji Rao and A. Lakshman, Quasi-complemented almost distributive lattice, Southeast Asian Bull. Math., 39(3)(2015), 311-319.
[7] M. H. Stone, Topological representation of distributive lattices and Brouwerian logics, asopis pro psiovn matematiky a fysiky, 67(1937-38), 1-25.
[8] M. Mandelker, Relative annihilators in lattices, Duke Math. J., 37(2)(1970), 377-386.
[9] M. Sambasiva Rao, Normal filters of distributive lattice, Bull. Sci. Logic, 41(3-4)(2012), 131-143.
[10] R. Munkres James, Topology, Prentice Hall of India Private Limited, 2005.
[11] S. Burris and H.P. Sankappanavar, A course in universal algebra, Springer-Verlag, 1980.
[12] S. Ramesh and G. Jogarao, Weak relatively complemented almost distributive lattices, (To appear).
[13] S. Ramesh, On almost distributive lattices, Doctoral thesis, Andhra University, 2009.
[14] T.P.Speed, Some remarks on a class of distributive lattices, J. Australian Math. Soc., 9(3-4)(1969), 289-296.
[15] T. S. Blyth, Ideals and filters of pseudo-complemented semi-lattices, Proc. Edn. Math. Soc., 23(3)(1980), 301-316.
[16] U.M Swamy and G.C Rao, Almost distributive lattices, J. Austral. Math. Soc., 31(1981), 77-91.
[17] W. H. Cornish, Normal lattices, J. Australian Math. Soc., 14(1972), 200-215.
[18] W. H. Cornish, Quasi complemented lattices, Comm. Math. Univer. Carolinae, 15(3)(1974), 501-511.
[19] Y. S. Pawar and I. A. Shaikh, On prime, minimal prime and annihilator ideal in an almost distributive lattices, European. J. Pure and Applied Maths., 6(1)(2013), 107-118.
[20] Y. S. Pawar, The space of maximal ideals in an almost distributive lattice, Int. Math. Forum., 6(28)(2011), 1387-1396.
[2] G. C. Rao and G. Nanaji Rao, Dense elements in almost distributive lattices, Southeast Asian Bull. Math., 27(6)(2004), 1081-1088.
[3] G. C. Rao and M. Sambasiva Rao, Annihilator ideal in almost distributive lattices, Int. Math. Forum., 4915)(2009), 733-746.
[4] G. C. Rao and M. Sambasiva Rao, Annulets in almost distributive lattices, Eur. J. Pure Appl. Math., 2(1)(2009), 58-72.
[5] G. C. Rao and S. Ravi Kumar, Minimal prime ideal in almost distributive lattices, Int. J. Contemp. Math. Sci., 4(10)(2009), 475-484.
[6] G. C. Rao, G. Nanaji Rao and A. Lakshman, Quasi-complemented almost distributive lattice, Southeast Asian Bull. Math., 39(3)(2015), 311-319.
[7] M. H. Stone, Topological representation of distributive lattices and Brouwerian logics, asopis pro psiovn matematiky a fysiky, 67(1937-38), 1-25.
[8] M. Mandelker, Relative annihilators in lattices, Duke Math. J., 37(2)(1970), 377-386.
[9] M. Sambasiva Rao, Normal filters of distributive lattice, Bull. Sci. Logic, 41(3-4)(2012), 131-143.
[10] R. Munkres James, Topology, Prentice Hall of India Private Limited, 2005.
[11] S. Burris and H.P. Sankappanavar, A course in universal algebra, Springer-Verlag, 1980.
[12] S. Ramesh and G. Jogarao, Weak relatively complemented almost distributive lattices, (To appear).
[13] S. Ramesh, On almost distributive lattices, Doctoral thesis, Andhra University, 2009.
[14] T.P.Speed, Some remarks on a class of distributive lattices, J. Australian Math. Soc., 9(3-4)(1969), 289-296.
[15] T. S. Blyth, Ideals and filters of pseudo-complemented semi-lattices, Proc. Edn. Math. Soc., 23(3)(1980), 301-316.
[16] U.M Swamy and G.C Rao, Almost distributive lattices, J. Austral. Math. Soc., 31(1981), 77-91.
[17] W. H. Cornish, Normal lattices, J. Australian Math. Soc., 14(1972), 200-215.
[18] W. H. Cornish, Quasi complemented lattices, Comm. Math. Univer. Carolinae, 15(3)(1974), 501-511.
[19] Y. S. Pawar and I. A. Shaikh, On prime, minimal prime and annihilator ideal in an almost distributive lattices, European. J. Pure and Applied Maths., 6(1)(2013), 107-118.
[20] Y. S. Pawar, The space of maximal ideals in an almost distributive lattice, Int. Math. Forum., 6(28)(2011), 1387-1396.
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2017-02-02
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