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A study on standard n-ideal of a lattice

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dc.contributor.advisor Azad, Prof. Dr. Md Abul kalam
dc.contributor.author Hossen, Md Imran
dc.date.accessioned 2019-07-07T09:40:13Z
dc.date.available 2019-07-07T09:40:13Z
dc.date.copyright 2019
dc.date.issued 2019-04
dc.identifier.other ID 1651501
dc.identifier.uri http://hdl.handle.net/20.500.12228/520
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 2019. en_US
dc.description Cataloged from PDF Version of Thesis.
dc.description Includes bibliographical references (pages 49-50).
dc.description.abstract Lattice theory is an important part of mathematics . Ideal lattice and n-ideal of a lattice have played many roles in development of lattice theory. Historically, lattice theory started with Boolean distributive lattices: as a result, the theory of ideal lattice and n-ideal of a lattice is the most extensive and most satisfying chapter in the history of lattice theory. Ideal lattice have provided the motivation for many results, in general lattice theory. Many conditions on lattices and on element and ideals of lattices are weakened forms of distributivity is imposed on lattices arising in various areas of mathematics, especially algebra. In lattice theory there are different classes of lattices known as variety of lattices. Class of Boolean lattice is of course most powerful variety. Throughout this thesis we will be concerned with another large variety known as the class of ideal lattice and n-ideal of a lattice have been studied by several authors. The realization of special role of ideal lattices moved to break with the traditional approach to lattice theory, which proceeds from partially ordered sets to general lattices, semi modular lattices, modular lattices and finally ideal lattices. In this thesis we give several result on ideal and n-ideal which will certainly extend and generalize many results in lattice theory. In order to review, we include definations, examples, solved problems and proof of some theorems. The thesis contains four chapter. Chapter 1 we have discussed the basic defination of relation, poset, lattice, complete lattice, convex sub lattice, complemented and relatively complemented lattice. We also proved that, Dual of a complete lattice is complete . Chapter 2 have discussed basic concept of ideal and n-ideal of lattice. Here we study the defination and examples of ideal and n-ideal. Some imprtant theorem like “If n is a neutral element of a lattice, then I (L) n is modular if and only if L is modular”. Chapter 3 we have discussed Standard element and n-ideals. We also discussed in this chapter Congruence relation. Chapter 4 deals with standard n-ideal and Principal n-ideal. This is the main part of this thesis work. In this chapter we have discussed some defination and some important theorems like “For a neutral element n and a standard n-ideal S and an n-ideal I, S I is also a standard n-ideal” . en_US
dc.description.statementofresponsibility Md Imran Hossen
dc.format.extent 50 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 Lattice Theory en_US
dc.subject Ideal Lattice en_US
dc.subject n-ideal of a Lattice en_US
dc.title A study on standard n-ideal of a lattice 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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