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# Study of Pseudocomplemented Lattice

 dc.contributor.advisor Azad, Dr. Md. Abul Kalam dc.contributor.author Rahman, Khaki Masudur dc.date.accessioned 2018-08-13T04:56:14Z dc.date.available 2018-08-13T04:56:14Z dc.date.copyright 2008 dc.date.issued 2008-06 dc.identifier.other ID 0051510 dc.identifier.uri http://hdl.handle.net/20.500.12228/354 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 Philosophy in Mathematics, June 2008. en_US dc.description Cataloged from PDF Version of Thesis. dc.description Includes bibliographical references (pages 87-88). dc.description.abstract This thesis studies the nature of Pseudocomplemented lattice. We can define a lattice in two ways; (i) Set theoretically and (ii) Algebraically. en_US Set theoretically: A poset is a lattice if for every a, b ϵ L both Sup {a,b} and Inf {a,b} exists in L. Algebraically : A nonempty set L with two binary operations ˄ and ˅ is called a lattice if ∀ a, b, C ϵ L. The following conditions hold. i. a ˄ a=a, a ˅ a= a ii. a ˄ b=b ˄ a ,a ˅ b=b ˅ a. iii. a ˄ (b ˄ c)=(a ˄ b) ˄ c, a ˅ (b ˅ c) = (a ˅ b) ˅ c, iv. a ˄ (a ˅ b)=a, a ˅ (a ˄ b)=a. In this thesis, we have studied several properties of pseudocomplemented lattices. Moreover, we give several results on pseudocomplemented lattices which certainly extend and generalize many results in lattice theory. In Chapter one, we have discussed posets, lattices and Ideals of a lattice which are explain with some examples and generalized many theorems of them. In chapter two, congruence of lattices, distributive lattices, Complemented lattices and Boolean algebra have been discussed, which are basic concept of this thesis. In chapter three we give a description of pseudocomplemented lattices. We have also studied distributive pseudocomplemented lattices and algebraic lattices. Pseudocompiemented lattices have been studied by G. Gratzer [7] and many other authors. Here we extend several results of G. Gratzer [7] to lattices. Chapter four introduces the concepts of stone lattices. Stone lattices have been studied by Gratzer [7], Katrinak [11] and many other authors. We have given a characterization of minimal prime ideals of pseudocompiemented distributive lattices. Chapter five introduces the concept of distributive and modular lattice with n-ideals. Here we include several characterizations of n-ideals. We have proved some interesting result which are generalizes several results on distributive ,modular and ideals of a lattices. Latif [20] in his thesis has introduced the concept of standard n-ideals of a lattice. We conclude this thesis with some more properties of standard and neutral n-ideals. dc.description.statementofresponsibility Khaki Masudur Rahman dc.format.extent 89 pages dc.language.iso en_US en_US dc.publisher Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh. en_US dc.subject Pseudocomplemented en_US dc.subject Lattice en_US dc.title Study of Pseudocomplemented Lattice en_US dc.type Thesis en_US dcterms.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.description.degree Master of Philosophy in Mathematics dc.contributor.department Department of Mathematics
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