On Weakly 1-Absorbing Primary Ideals of Commutative Rings
Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is called a weakly 1-absorbing primary ideal if whenever nonunit elements a, b, c ∈ R and 0 ≠ abc ∈ I, the...
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2022
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/25072 |
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إضافة وسم
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| _version_ | 1864513441987821568 |
|---|---|
| author | Badawi, Ayman |
| author2 | Celikel, Ece Yetkin |
| author2_role | author |
| author_facet | Badawi, Ayman Celikel, Ece Yetkin |
| author_role | author |
| dc.creator.none.fl_str_mv | Badawi, Ayman Celikel, Ece Yetkin |
| dc.date.none.fl_str_mv | 2022-11-28T11:50:16Z 2022-11-28T11:50:16Z 2022 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Badawi, A., & Yetkin Celikel, E. (2022). On Weakly 1-Absorbing Primary Ideals of Commutative Rings. In Algebra Colloquium (Vol. 29, Issue 02, pp. 189–202). World Scientific. https://doi.org/10.1142/s1005386722000153 0219-1733 http://hdl.handle.net/11073/25072 10.1142/s1005386722000153 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | World Scientific |
| dc.relation.none.fl_str_mv | http://hdl.handle.net/11073/25072 |
| dc.subject.none.fl_str_mv | 1-absorbing primary ideal 2-absorbing primary ideal 2-absorbing ideal Weakly 2-absorbing primary ideal Weakly primary |
| dc.title.none.fl_str_mv | On Weakly 1-Absorbing Primary Ideals of Commutative Rings |
| dc.type.none.fl_str_mv | Peer-Reviewed Postprint info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is called a weakly 1-absorbing primary ideal if whenever nonunit elements a, b, c ∈ R and 0 ≠ abc ∈ I, then ab ∈ I or c ∈ √I. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. Furthermore, we give the correct version of a result on 1-absorbing primary ideals of commutative rings. |
| format | article |
| id | aus_9022a5777d941adef8a0b61635754e6b |
| identifier_str_mv | Badawi, A., & Yetkin Celikel, E. (2022). On Weakly 1-Absorbing Primary Ideals of Commutative Rings. In Algebra Colloquium (Vol. 29, Issue 02, pp. 189–202). World Scientific. https://doi.org/10.1142/s1005386722000153 0219-1733 10.1142/s1005386722000153 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/25072 |
| publishDate | 2022 |
| publisher.none.fl_str_mv | World Scientific |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | On Weakly 1-Absorbing Primary Ideals of Commutative RingsBadawi, AymanCelikel, Ece Yetkin1-absorbing primary ideal2-absorbing primary ideal2-absorbing idealWeakly 2-absorbing primary idealWeakly primaryLet R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is called a weakly 1-absorbing primary ideal if whenever nonunit elements a, b, c ∈ R and 0 ≠ abc ∈ I, then ab ∈ I or c ∈ √I. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. Furthermore, we give the correct version of a result on 1-absorbing primary ideals of commutative rings.World Scientific2022-11-28T11:50:16Z2022-11-28T11:50:16Z2022Peer-ReviewedPostprintinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfBadawi, A., & Yetkin Celikel, E. (2022). On Weakly 1-Absorbing Primary Ideals of Commutative Rings. In Algebra Colloquium (Vol. 29, Issue 02, pp. 189–202). World Scientific. https://doi.org/10.1142/s10053867220001530219-1733http://hdl.handle.net/11073/2507210.1142/s1005386722000153en_UShttp://hdl.handle.net/11073/25072oai:repository.aus.edu:11073/250722024-08-22T12:01:51Z |
| spellingShingle | On Weakly 1-Absorbing Primary Ideals of Commutative Rings Badawi, Ayman 1-absorbing primary ideal 2-absorbing primary ideal 2-absorbing ideal Weakly 2-absorbing primary ideal Weakly primary |
| status_str | publishedVersion |
| title | On Weakly 1-Absorbing Primary Ideals of Commutative Rings |
| title_full | On Weakly 1-Absorbing Primary Ideals of Commutative Rings |
| title_fullStr | On Weakly 1-Absorbing Primary Ideals of Commutative Rings |
| title_full_unstemmed | On Weakly 1-Absorbing Primary Ideals of Commutative Rings |
| title_short | On Weakly 1-Absorbing Primary Ideals of Commutative Rings |
| title_sort | On Weakly 1-Absorbing Primary Ideals of Commutative Rings |
| topic | 1-absorbing primary ideal 2-absorbing primary ideal 2-absorbing ideal Weakly 2-absorbing primary ideal Weakly primary |
| url | http://hdl.handle.net/11073/25072 |