On the probability and graph of some finite rings of matrices
The study on probability theory in finite rings has been an interest of various researchers. One of the probabilities that has caught their attention is the probability that two elements of a ring have product zero. In this study, the probability is determined for a finite ring R of matrices over in...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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2020
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| Online Access: | http://eprints.utm.my/90860/1/NurhidayahZaid2020_OntheProbabilityandGraphofSomeFinite.pdf |
| _version_ | 1796865113868730368 |
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| author | Zaid, Nurhidayah Sarmin, Nor Haniza Salih Khasraw, Sanhan Muhammad |
| author_facet | Zaid, Nurhidayah Sarmin, Nor Haniza Salih Khasraw, Sanhan Muhammad |
| author_sort | Zaid, Nurhidayah |
| collection | ePrints |
| description | The study on probability theory in finite rings has been an interest of various researchers. One of the probabilities that has caught their attention is the probability that two elements of a ring have product zero. In this study, the probability is determined for a finite ring R of matrices over integers modulo four. First, the annihilators of R are determined with the assistance of Groups, Algorithms and Programming (GAP) software and then the probability is calculated using the definition. Next, by using the results obtained, the zero divisor graph of the ring R is constructed. A zero divisor graph is defined as a graph in which the zero divisors of R are its vertices and two vertices are connected by an edge if their product is zero. |
| first_indexed | 2024-03-05T20:52:01Z |
| format | Conference or Workshop Item |
| id | utm.eprints-90860 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T20:52:01Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | utm.eprints-908602021-05-31T13:40:03Z http://eprints.utm.my/90860/ On the probability and graph of some finite rings of matrices Zaid, Nurhidayah Sarmin, Nor Haniza Salih Khasraw, Sanhan Muhammad QA Mathematics The study on probability theory in finite rings has been an interest of various researchers. One of the probabilities that has caught their attention is the probability that two elements of a ring have product zero. In this study, the probability is determined for a finite ring R of matrices over integers modulo four. First, the annihilators of R are determined with the assistance of Groups, Algorithms and Programming (GAP) software and then the probability is calculated using the definition. Next, by using the results obtained, the zero divisor graph of the ring R is constructed. A zero divisor graph is defined as a graph in which the zero divisors of R are its vertices and two vertices are connected by an edge if their product is zero. 2020-10-06 Conference or Workshop Item PeerReviewed application/pdf en http://eprints.utm.my/90860/1/NurhidayahZaid2020_OntheProbabilityandGraphofSomeFinite.pdf Zaid, Nurhidayah and Sarmin, Nor Haniza and Salih Khasraw, Sanhan Muhammad (2020) On the probability and graph of some finite rings of matrices. In: 27th National Symposium on Mathematical Sciences, SKSM 2019, 26 November 2019 - 27 November 2019, Tenera Hotel, Bangi, Selangor, Malaysia. http://dx.doi.org/10.1063/5.0018067 |
| spellingShingle | QA Mathematics Zaid, Nurhidayah Sarmin, Nor Haniza Salih Khasraw, Sanhan Muhammad On the probability and graph of some finite rings of matrices |
| title | On the probability and graph of some finite rings of matrices |
| title_full | On the probability and graph of some finite rings of matrices |
| title_fullStr | On the probability and graph of some finite rings of matrices |
| title_full_unstemmed | On the probability and graph of some finite rings of matrices |
| title_short | On the probability and graph of some finite rings of matrices |
| title_sort | on the probability and graph of some finite rings of matrices |
| topic | QA Mathematics |
| url | http://eprints.utm.my/90860/1/NurhidayahZaid2020_OntheProbabilityandGraphofSomeFinite.pdf |
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