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Study on Standard Ideal and Homomorphism Theorem of a Nearlattice

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dc.contributor.advisor Rahman, Dr. Md. Zaidur
dc.contributor.author Hossain, G.M. Jahid
dc.date.accessioned 2018-05-27T10:50:02Z
dc.date.available 2018-05-27T10:50:02Z
dc.date.copyright 2017
dc.date.issued 2017-04
dc.identifier.other ID 1551553
dc.identifier.uri http://hdl.handle.net/20.500.12228/173
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, April 2017. en_US
dc.description Cataloged from PDF Version of Thesis.
dc.description Includes bibliographical references (pages 47-48).
dc.description.abstract In this thesis the standard ideal of a nearlattices 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 Hickman [4] referred this property as the upper bound property, and a semilattice of this nature as a semilattice with the upperbound property. Cornish and Noor [5] preferred to call these semilattices as nearlattices, as the behavior 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. Geatzer [12] studied the non-distributive lattice by introducing the concept of distributive, standard and neutral elements in lattices. Cornish and Noor [5] extended those concepts for nearlattices to study non-distributive nearlattices. This thesis extend the concept of standard ideal of a nearlattices. We also extend the homomorphism theorem of lattices to nearlattices. Finally we generalize two isomorphism theorems of Gratzer, G. and Schmidt, E. T [14] to nearlattices. en_US
dc.description.statementofresponsibility G.M. Jahid Hossain
dc.format.extent 48 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 Homomorphism Theorem en_US
dc.subject Nearlattice en_US
dc.title Study on Standard Ideal and Homomorphism Theorem of a 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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