Semi r-ideals of commutative rings
For commutative rings with identity, we introduce and study the concept of semi r-ideals which is a kind of generalization of both r-ideals and semiprime ideals. A proper ideal I of a commutative ring R is called semi r-ideal if whenever a2 ∈ I and AnnR(a) = 0, then a ∈ I. Several properties and cha...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-03-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2023-0022 |
| _version_ | 1827968992779698176 |
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| author | Khashan Hani A. Celikel Ece Yetkin |
| author_facet | Khashan Hani A. Celikel Ece Yetkin |
| author_sort | Khashan Hani A. |
| collection | DOAJ |
| description | For commutative rings with identity, we introduce and study the concept of semi r-ideals which is a kind of generalization of both r-ideals and semiprime ideals. A proper ideal I of a commutative ring R is called semi r-ideal if whenever a2 ∈ I and AnnR(a) = 0, then a ∈ I. Several properties and characterizations of this class of ideals are determined. In particular, we investigate semi r-ideal under various contexts of constructions such as direct products, localizations, homomorphic images, idealizations and amalagamations rings. We extend semi r-ideals of rings to semi r-submodules of modules and clarify some of their properties. Moreover, we define submodules satisfying the D-annihilator condition and justify when they are semi r-submodules. |
| first_indexed | 2024-04-09T18:30:05Z |
| format | Article |
| id | doaj.art-b32b8642e7f94a6f86c3af23d03961b6 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-09T18:30:05Z |
| publishDate | 2023-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-b32b8642e7f94a6f86c3af23d03961b62023-04-11T17:19:08ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352023-03-0131210112610.2478/auom-2023-0022Semi r-ideals of commutative ringsKhashan Hani A.0Celikel Ece Yetkin11Department of Mathematics, Faculty of Science, Al al-Bayt University, Al Mafraq, Jordan.2Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu UniversityGaziantep, Turkey.For commutative rings with identity, we introduce and study the concept of semi r-ideals which is a kind of generalization of both r-ideals and semiprime ideals. A proper ideal I of a commutative ring R is called semi r-ideal if whenever a2 ∈ I and AnnR(a) = 0, then a ∈ I. Several properties and characterizations of this class of ideals are determined. In particular, we investigate semi r-ideal under various contexts of constructions such as direct products, localizations, homomorphic images, idealizations and amalagamations rings. We extend semi r-ideals of rings to semi r-submodules of modules and clarify some of their properties. Moreover, we define submodules satisfying the D-annihilator condition and justify when they are semi r-submodules.https://doi.org/10.2478/auom-2023-0022semiprime idealsemiprime submodulesemi r-idealsemi r-submoduleprimary 13a15, 16p40secondary 16d60 |
| spellingShingle | Khashan Hani A. Celikel Ece Yetkin Semi r-ideals of commutative rings Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica semiprime ideal semiprime submodule semi r-ideal semi r-submodule primary 13a15, 16p40 secondary 16d60 |
| title | Semi r-ideals of commutative rings |
| title_full | Semi r-ideals of commutative rings |
| title_fullStr | Semi r-ideals of commutative rings |
| title_full_unstemmed | Semi r-ideals of commutative rings |
| title_short | Semi r-ideals of commutative rings |
| title_sort | semi r ideals of commutative rings |
| topic | semiprime ideal semiprime submodule semi r-ideal semi r-submodule primary 13a15, 16p40 secondary 16d60 |
| url | https://doi.org/10.2478/auom-2023-0022 |
| work_keys_str_mv | AT khashanhania semiridealsofcommutativerings AT celikeleceyetkin semiridealsofcommutativerings |