Noetherian module matrix over commutative ring

Algebraic structure is a set together with one or more binary operations that satisfy some axioms of the binary operations, for example groups, rings, and modules. Modules M is Noetherian modules if the ascending chain condition hold for every submodules of M . Let R be a ring and M mxn (R) is se...

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Format:	Thesis
Language:	English
Subjects:	Algebra Commutative algebra Set theory
Online Access:	http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/1/Page%201-24.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/2/Full%20text.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/3/Declaration%20Form.pdf
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spelling	my-unimap-766282022-10-26T01:05:41Z Noetherian module matrix over commutative ring Ahmad Kadri, Junoh, Dr. Algebraic structure is a set together with one or more binary operations that satisfy some axioms of the binary operations, for example groups, rings, and modules. Modules M is Noetherian modules if the ascending chain condition hold for every submodules of M . Let R be a ring and M mxn (R) is set of matrices which the entries are element of R , if m = n then M n (R) together with addition and multiplication matrix is a ring called matrix ring. The aim of this study is to construct the algebraic structures from the set of matrices in order to fulfill every axioms of modules. The requirements for matrix ring M n (R) and module matrix M mxn (R) that satisfy the Noetherian conditions are investigated. The Noetherian term of algebraic structures will be studied, then the algebraic structure for the entries of the matrix will be determined such that satisfy the Noetherian module. This study, it has been shown that modules M mxn (R) is satisfy Noetherian R - module if the algebraic structure (R,+) is Noetherian group and module M mxn (R) is also Artinian module. The facts regarding homomorphism modules of M mxn (R) are also obtained Universiti Malaysia Perlis (UniMAP) Thesis en http://dspace.unimap.edu.my:80/xmlui/handle/123456789/76628 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/4/license.txt 8a4605be74aa9ea9d79846c1fba20a33 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/1/Page%201-24.pdf f16438f8197408c06ec3ec5726d66849 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/2/Full%20text.pdf 3175b26805cd1948ac8d9ec04aadd905 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/3/Declaration%20Form.pdf 9a77feddca0c6512592c9e1b1c509303 Universiti Malaysia Perlis (UniMAP) Algebra Commutative algebra Set theory Institute of Engineering Mathematics
institution	Universiti Malaysia Perlis
collection	UniMAP Institutional Repository
language	English
advisor	Ahmad Kadri, Junoh, Dr.
topic	Algebra Commutative algebra Set theory
spellingShingle	Algebra Commutative algebra Set theory Noetherian module matrix over commutative ring
description	Algebraic structure is a set together with one or more binary operations that satisfy some axioms of the binary operations, for example groups, rings, and modules. Modules M is Noetherian modules if the ascending chain condition hold for every submodules of M . Let R be a ring and M mxn (R) is set of matrices which the entries are element of R , if m = n then M n (R) together with addition and multiplication matrix is a ring called matrix ring. The aim of this study is to construct the algebraic structures from the set of matrices in order to fulfill every axioms of modules. The requirements for matrix ring M n (R) and module matrix M mxn (R) that satisfy the Noetherian conditions are investigated. The Noetherian term of algebraic structures will be studied, then the algebraic structure for the entries of the matrix will be determined such that satisfy the Noetherian module. This study, it has been shown that modules M mxn (R) is satisfy Noetherian R - module if the algebraic structure (R,+) is Noetherian group and module M mxn (R) is also Artinian module. The facts regarding homomorphism modules of M mxn (R) are also obtained
format	Thesis
title	Noetherian module matrix over commutative ring
title_short	Noetherian module matrix over commutative ring
title_full	Noetherian module matrix over commutative ring
title_fullStr	Noetherian module matrix over commutative ring
title_full_unstemmed	Noetherian module matrix over commutative ring
title_sort	noetherian module matrix over commutative ring
granting_institution	Universiti Malaysia Perlis (UniMAP)
granting_department	Institute of Engineering Mathematics
url	http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/1/Page%201-24.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/2/Full%20text.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/76628/3/Declaration%20Form.pdf
_version_	1776104268181274624

Noetherian module matrix over commutative ring

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