Filters of lattices with respect to a congruence

M. Sambasiva Rao; Abd El-Mohsen Badawy

ArticleOriginal scientific text

Title

Filters of lattices with respect to a congruence

Authors ¹, ²

Affiliations

Department of Mathematics, M.V.G.R. College of Engineering, Chintalavalasa Vizianagaram, Andhra Pradesh, India-535005
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Abstract

Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of

L_{/ θ}

is obtained.

Keywords

ENG

congruence, filter, closure operator, θ-filter, congruence lattice

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Title

Filters of lattices with respect to a congruence

Affiliations

Abstract

Keywords

Bibliography