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Let R be a commutative ring with identity 1 = 0. We say that a ring is a chained ring if either x j y or y j x for all x; y 2 R. The set of the zero-divisors of a ring <br /> <br /> <br /> is Z(R), and Nil(R) its ideal of nilpotent elements. The zero-divisor graph of R is T(R) =...

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Main Author: NURCAHYANI (NIM : 10106042); Pembimbing Tugas Akhir : Prof. Dr. Irawati, ELIH
Format: Final Project
Language:Indonesia
Online Access:https://digilib.itb.ac.id/gdl/view/15527
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Institution: Institut Teknologi Bandung
Language: Indonesia
id id-itb.:15527
spelling id-itb.:155272017-09-27T11:43:10Z#TITLE_ALTERNATIVE# NURCAHYANI (NIM : 10106042); Pembimbing Tugas Akhir : Prof. Dr. Irawati, ELIH Indonesia Final Project INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/15527 Let R be a commutative ring with identity 1 = 0. We say that a ring is a chained ring if either x j y or y j x for all x; y 2 R. The set of the zero-divisors of a ring <br /> <br /> <br /> is Z(R), and Nil(R) its ideal of nilpotent elements. The zero-divisor graph of R is T(R) = Z(R) n (0), with distinct vertices x and y adjacent if and only if xy = 0. <br /> <br /> <br /> In this manuscript, we show that the diameter of the zero-divisor graph of a chained ring is diam (T(R)) < 2. The diameter of the zero-divisor graph of a ring such that <br /> <br /> <br /> the prime ideals of R contained in Z(R) are linearly ordered is 2. text
institution Institut Teknologi Bandung
building Institut Teknologi Bandung Library
continent Asia
country Indonesia
Indonesia
content_provider Institut Teknologi Bandung
collection Digital ITB
language Indonesia
description Let R be a commutative ring with identity 1 = 0. We say that a ring is a chained ring if either x j y or y j x for all x; y 2 R. The set of the zero-divisors of a ring <br /> <br /> <br /> is Z(R), and Nil(R) its ideal of nilpotent elements. The zero-divisor graph of R is T(R) = Z(R) n (0), with distinct vertices x and y adjacent if and only if xy = 0. <br /> <br /> <br /> In this manuscript, we show that the diameter of the zero-divisor graph of a chained ring is diam (T(R)) < 2. The diameter of the zero-divisor graph of a ring such that <br /> <br /> <br /> the prime ideals of R contained in Z(R) are linearly ordered is 2.
format Final Project
author NURCAHYANI (NIM : 10106042); Pembimbing Tugas Akhir : Prof. Dr. Irawati, ELIH
spellingShingle NURCAHYANI (NIM : 10106042); Pembimbing Tugas Akhir : Prof. Dr. Irawati, ELIH
#TITLE_ALTERNATIVE#
author_facet NURCAHYANI (NIM : 10106042); Pembimbing Tugas Akhir : Prof. Dr. Irawati, ELIH
author_sort NURCAHYANI (NIM : 10106042); Pembimbing Tugas Akhir : Prof. Dr. Irawati, ELIH
title #TITLE_ALTERNATIVE#
title_short #TITLE_ALTERNATIVE#
title_full #TITLE_ALTERNATIVE#
title_fullStr #TITLE_ALTERNATIVE#
title_full_unstemmed #TITLE_ALTERNATIVE#
title_sort #title_alternative#
url https://digilib.itb.ac.id/gdl/view/15527
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