On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative rings
Consider a commutative ring with unity denoted as [Formula: see text]. An ideal I of a ring [Formula: see text] is called an annihilating ideal if there exists a non-zero element [Formula: see text] such that rI = 0. An ideal J of [Formula: see text] is called an essential ideal if J has a non-zero...
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Taylor & Francis Group
2025-12-01
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| Series: | Journal of Taibah University for Science |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2025.2455215 |
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| author | Nadeem ur Rehman Shabir Ahmad Mir Mohd Nazim Nazim Nazim |
| author_facet | Nadeem ur Rehman Shabir Ahmad Mir Mohd Nazim Nazim Nazim |
| author_sort | Nadeem ur Rehman |
| collection | DOAJ |
| description | Consider a commutative ring with unity denoted as [Formula: see text]. An ideal I of a ring [Formula: see text] is called an annihilating ideal if there exists a non-zero element [Formula: see text] such that rI = 0. An ideal J of [Formula: see text] is called an essential ideal if J has a non-zero intersection with every other non-zero ideal of [Formula: see text]. The sum-annihilating essential ideal graph of [Formula: see text], denoted by [Formula: see text], is a graph whose vertex set is the set of all non-zero annihilating ideals of [Formula: see text] and two distinct vertices I and J are adjacent whenever [Formula: see text] is an essential ideal of [Formula: see text]. In this research paper, we have determined the metric dimension of [Formula: see text] for various classifications of rings. Furthermore, we have classified Artinian rings [Formula: see text] for which the sum-annihilating essential ideal graph exhibits projective properties. |
| format | Article |
| id | doaj-art-e38de422f6fc4ca4919ccb40efc0fa87 |
| institution | Kabale University |
| issn | 1658-3655 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj-art-e38de422f6fc4ca4919ccb40efc0fa872025-01-29T19:05:47ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552025-12-0119110.1080/16583655.2025.2455215On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative ringsNadeem ur Rehman0Shabir Ahmad Mir1Mohd Nazim2Nazim Nazim3Department of Mathematics, Aligarh Muslim University, Aligarh, IndiaSchool of Basic and Applied Sciences, Faculty of Science and Technology, JSPM University, Pune, IndiaSchool of Basic and Applied Sciences, Faculty of Science and Technology, JSPM University, Pune, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaConsider a commutative ring with unity denoted as [Formula: see text]. An ideal I of a ring [Formula: see text] is called an annihilating ideal if there exists a non-zero element [Formula: see text] such that rI = 0. An ideal J of [Formula: see text] is called an essential ideal if J has a non-zero intersection with every other non-zero ideal of [Formula: see text]. The sum-annihilating essential ideal graph of [Formula: see text], denoted by [Formula: see text], is a graph whose vertex set is the set of all non-zero annihilating ideals of [Formula: see text] and two distinct vertices I and J are adjacent whenever [Formula: see text] is an essential ideal of [Formula: see text]. In this research paper, we have determined the metric dimension of [Formula: see text] for various classifications of rings. Furthermore, we have classified Artinian rings [Formula: see text] for which the sum-annihilating essential ideal graph exhibits projective properties.https://www.tandfonline.com/doi/10.1080/16583655.2025.2455215Metric dimensioncrosscapsum-annihilating essential ideal graphcommutative rings05C1005C12 |
| spellingShingle | Nadeem ur Rehman Shabir Ahmad Mir Mohd Nazim Nazim Nazim On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative rings Journal of Taibah University for Science Metric dimension crosscap sum-annihilating essential ideal graph commutative rings 05C10 05C12 |
| title | On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative rings |
| title_full | On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative rings |
| title_fullStr | On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative rings |
| title_full_unstemmed | On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative rings |
| title_short | On metric dimension and crosscap analysis of sum-annihilating essential ideal graph of commutative rings |
| title_sort | on metric dimension and crosscap analysis of sum annihilating essential ideal graph of commutative rings |
| topic | Metric dimension crosscap sum-annihilating essential ideal graph commutative rings 05C10 05C12 |
| url | https://www.tandfonline.com/doi/10.1080/16583655.2025.2455215 |
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