JOURNAL OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4866, ISSN (o) 2303-4947 www.imvibl.org /JOURNALS / JOURNAL Vol. 7(2017), 37-51 DOI: 10.7251/JIMVI1701037S Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) NORMAL FILTERS IN ALMOST DISTRIBUTIVE LATTICES Ramesh Sirisetti and G. Jogarao Abstract. In this paper we introduce normal filters and normlets in an almost distributive lattice with dense elements and reinforce them in both algebraical and topological aspects. 1. Introduction and Preliminaries The structure of distributive lattice is exponentially enrich and has smooth nature. A vast number of researchers broadly studied the class of distributive lattice in different aspects. In [7, 8, 9, 15, 16, 17, 18], the authors initiated the ideal/ filter/ congruence theory in a distributive lattice and they have showed some special class of distributive lattices like normal lattices, quasi complemented distributive lattices etc. Some of the authors take a broad view of the structure of distributive lattice in different aspects. In this context, U. M. Swamy and G. C. Rao [16] generalized the structure of distributive lattice as a common abstraction of lattice theoretic and ring theoretic aspects called as almost distributive lattice in 1981. Later, the authors [2, 3, 4, 5, 6, 12, 19, 20] analogously extended some concepts to almost distributive lattices which are in distributive lattices. In this paper we mainly concentrate on filters in an almost distributive lattice with dense elements. In this first section, we collect some preliminary results on almost distributive lattices which are useful in the sequent sections. In second section, we introduce normal filters in an almost distributive lattice and certain examples are given and derive some properties on the class of normal filters. In third section, we study the class of normlets in an almost distributive lattice and obtain several equivalent conditions for a filter to become a normlet. In fourth 2010 Mathematics Subject Classification. Primary 06D99; Secondary 06D15. Key words and phrases. Normal filter, dense element, weak relatively complemented almost distributive lattice and the Hull-kernel topology. 37