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V. Slavik [8] introduced the concept of ideal(filter) in a skew lattice. In this paper we introduce the concept of a filter in a skew lattice which includes the class of all filters in the sense of Slavik. Also we introduce the concept of prime filter in a skew lattice and study the distributive skew lattices and the space of prime filters of a distributive skew lattice with hull-kernel topology. [ABSTRACT FROM AUTHOR]

In this paper characterization for non-symmetric skew lattices, with number of elements less than or equal to ten, is obtained. Non-Symmetric skew lattices with least number of elements are described, which are at the same time the examples to show that the converse of the Spink's theorem ([1, Corollary 4]) however is not true. [ABSTRACT FROM AUTHOR]

In this paper we introduce several concepts which are useful in the development of the theory of Generalised lattices, including the notions of Strong ideals, Strong filters, R--Strong ideals, R--Strong filters, Homomorphisms, Strong homomorphisms and Strong congruences in Generalised lattices. We also introduce the concepts of Congruence and Modularity in Posets. [ABSTRACT FROM AUTHOR]