Analisis latis modular pada himpunan matriks Boolean n x n

Hotmah, Nurul (2013) Analisis latis modular pada himpunan matriks Boolean n x n. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA :

Sistem aljabar dengan dua operasi biner yang memenuhi sifat tertutup, komutatif, asosiatif dan absorpsi disebut latis. Selanjutnya dalam latis terdapat beberapa kelas istimewa, di antaranya adalah latis distributif, latis modular dan latis semi modular. Akan tetapi dalam perkembangannya, latis masih jarang sekali dijadikan materi penelitian, terlebih mengenai latis istimewa, seperti halnya latis modular. Oleh karena itu, untuk memberi warna baru pada materi latis, maka dalam penelitian ini penulis menggunakan himpunan matriks Boolean dalam menganalisis sifat-sifat dan beberapa teorema yang berlaku pada latis modular dengan definisi tertentu.

Dengan mendefinisikan operasi matriks dan keterurutan parsial pada himpunan matriks Boolean n x n, maka himpunan matriks Boolean dengan entri semua anggota dari aljabar Boolean yang disertai dua operasi biner ⋃ dan ∩ adalah latis. Selanjutnya himpunan matriks Boolean dengan dua operasi biner ⋃ dan ∩ juga memenuhi sifat-sifat latis modular.

ENGLISH :

Algebraic system with two binary operations that satisfy the closed, commutative, associative and absorption properties is called lattices. Next in lattices there are some special classes, such as distributive lattices, modular lattices and semi-modular lattices. But in its development, lattices still rarely used as research material, especially on special lattices, as well as modular lattices. Furthermore, to give a new knowledge to the material lattices, so in this research the authors used the set of Boolean matrices in analyzing the properties and some of the theorems that apply to modular lattices with specific definitions.

By defining the matrices operation and partially ordered set on the set of n×n the matrices operation and partially ordered set on the set of Boolean matrices, then the set of Boolean matrices with entries all elemen of Boolean algebra,with two binary operations ⋃ and ⋂ is lattices. Furthermore, the set of Boolean matrices with two binary operations ⋃ and ⋂ also satisfy the modular lattice properties.

Item Type: Thesis (Undergraduate)
Supervisor: Turmudi, Turmudi and Irawan, Wahyu Hengky
Keywords: Latis Modular; Matriks Boolean; Modular Lattices; Boolean Matrices
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Dinda Akromatul Akhadiyah
Date Deposited: 30 May 2017 07:45
Last Modified: 30 May 2017 07:45
URI: http://etheses.uin-malang.ac.id/id/eprint/6878

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