Classification of Rings with Toroidal and Projective Coannihilator Graph
Let S be a commutative ring with unity, and a set of nonunit elements is denoted by WS. The coannihilator graph of S, denoted by AG′S, is an undirected graph with vertex set WS∗ (set of all nonzero nonunit elements of S), and α∼β is an edge of AG′S⇔α∉αβS or β∉αβS, where δS denotes the principal idea...
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4384683 |
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| author | Abdulaziz M. Alanazi Mohd Nazim Nadeem Ur Rehman |
| author_facet | Abdulaziz M. Alanazi Mohd Nazim Nadeem Ur Rehman |
| author_sort | Abdulaziz M. Alanazi |
| collection | DOAJ |
| description | Let S be a commutative ring with unity, and a set of nonunit elements is denoted by WS. The coannihilator graph of S, denoted by AG′S, is an undirected graph with vertex set WS∗ (set of all nonzero nonunit elements of S), and α∼β is an edge of AG′S⇔α∉αβS or β∉αβS, where δS denotes the principal ideal generated by δ∈S. In this study, we first classify finite ring S, for which AG′S is isomorphic to some well-known graph. Then, we characterized the finite ring S, for which AG′S is toroidal or projective. |
| format | Article |
| id | doaj-art-c11f453178bc45b8aef46daf600d1718 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c11f453178bc45b8aef46daf600d17182025-02-03T01:25:09ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/43846834384683Classification of Rings with Toroidal and Projective Coannihilator GraphAbdulaziz M. Alanazi0Mohd Nazim1Nadeem Ur Rehman2Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaLet S be a commutative ring with unity, and a set of nonunit elements is denoted by WS. The coannihilator graph of S, denoted by AG′S, is an undirected graph with vertex set WS∗ (set of all nonzero nonunit elements of S), and α∼β is an edge of AG′S⇔α∉αβS or β∉αβS, where δS denotes the principal ideal generated by δ∈S. In this study, we first classify finite ring S, for which AG′S is isomorphic to some well-known graph. Then, we characterized the finite ring S, for which AG′S is toroidal or projective.http://dx.doi.org/10.1155/2021/4384683 |
| spellingShingle | Abdulaziz M. Alanazi Mohd Nazim Nadeem Ur Rehman Classification of Rings with Toroidal and Projective Coannihilator Graph Journal of Mathematics |
| title | Classification of Rings with Toroidal and Projective Coannihilator Graph |
| title_full | Classification of Rings with Toroidal and Projective Coannihilator Graph |
| title_fullStr | Classification of Rings with Toroidal and Projective Coannihilator Graph |
| title_full_unstemmed | Classification of Rings with Toroidal and Projective Coannihilator Graph |
| title_short | Classification of Rings with Toroidal and Projective Coannihilator Graph |
| title_sort | classification of rings with toroidal and projective coannihilator graph |
| url | http://dx.doi.org/10.1155/2021/4384683 |
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