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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2025-12-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2025.2455215 |
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| Summary: | 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. |
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| ISSN: | 1658-3655 |