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# A study on Weakly Complemented Nearlattice

 dc.contributor.advisor Rahrnan, Prof. Dr. Md. Zaidur dc.contributor.author Rahman, Mahfuza dc.date.accessioned 2018-08-07T10:25:05Z dc.date.available 2018-08-07T10:25:05Z dc.date.copyright 2016 dc.date.issued 2016-07 dc.identifier.other ID 1451555 dc.identifier.uri http://hdl.handle.net/20.500.12228/190 dc.description This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Science in Mathematics, July 2016. en_US dc.description Cataloged from PDF Version of Thesis. dc.description Includes bibliographical references (pages 63-65). dc.description.abstract In this thesis study of the nature of the weakly complemented nearlattice is presented. By a nearlattice S we will always mean a meet semilattice together with the property that any two elements possessing a common upper bound, have a supremum. Cornish and referred this property as the upper bound property, and a semilattice of this nature as a semilattice with the upperbound property. Cornish and Noor [8] preferred to Hickman [7] call these semilattices as nearlattices, as the behaviour of such a semilattice is close to that of a lattice than an ordinary semilattice. Of course a nearlattice with a largest element is a lattice. Since any semilattice satisfying the descending chain condition has the upper bound property, so all finite semilattices are nearlattices. In lattice theory, it is always very difficult to study the non-distributive and non-modular lattices. Gratzer [12] studied the non-distributive lattices by introducing the concept of distributive, standard and neutral elements in lattices. Cornish and Noor [8] extended those concepts for nearlattices to study non-distributive nearlattices. On the other hand, J.C Varlet [33] studied another class of non-distributive lattices with 0 by introducing the concept of 0-distributivity. In fact this concept also generalizes the idea of pseudocomplement in a general lattice. In this thesis we have extended the concept of weakly complemented nearlattice in terms of homomorphism theorem. en_US dc.description.statementofresponsibility Mahfuza Rahman dc.format.extent 65 pages dc.language.iso en_US en_US dc.publisher Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh en_US dc.rights Khulna University of Engineering & Technology (KUET) thesis/dissertation/internship reports are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. dc.subject Lattice en_US dc.subject Nearlattice en_US dc.subject Distributive Neaiiattice en_US dc.subject Homomorphism Theorem en_US dc.title A study on Weakly Complemented Nearlattice en_US dc.type Thesis en_US dc.description.degree Master of Science in Mathematics dc.contributor.department Department of Mathematics
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