On n-semiprimary ideals and n-pseudo valuation domains
Let R be a commutative ring with 1 ≠ 0 and n a positive integer. A proper ideal I of R is an n-semiprimary ideal of R if whenever x^n y^n ∈ I for x, y ∈ R, then x^n ∈ I or y^n ∈ I. Let R be an integral domain with quotient field K. A proper ideal I of R is an n-powerful ideal of R if whenever x^n y^...
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| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2020
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/25071 |
| الوسوم: |
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| _version_ | 1864513443380330496 |
|---|---|
| author | Anderson, David F. |
| author2 | Badawi, Ayman |
| author2_role | author |
| author_facet | Anderson, David F. Badawi, Ayman |
| author_role | author |
| dc.creator.none.fl_str_mv | Anderson, David F. Badawi, Ayman |
| dc.date.none.fl_str_mv | 2020-08-14 2022-11-28T11:44:38Z 2022-11-28T11:44:38Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Anderson, D. F., & Badawi, A. (2020). On n-semiprimary ideals and n-pseudo valuation domains. In Communications in Algebra (Vol. 49, Issue 2, pp. 500–520). Informa UK Limited. https://doi.org/10.1080/00927872.2020.1803345 1532-4125 http://hdl.handle.net/11073/25071 10.1080/00927872.2020.1803345 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | Taylor and Francis |
| dc.relation.none.fl_str_mv | https://doi.org/10.1080/00927872.2020.1803345 |
| dc.subject.none.fl_str_mv | Prime ideal 2-absorbing ideal n-absorbing ideal Primary ideal Semiprimary ideal Radical ideal Powerful ideal Valuation domain Almost valuation domain Pseudo-valuation domain Almost pseudo-valuation domain Pseudo-almost valuation domain |
| dc.title.none.fl_str_mv | On n-semiprimary ideals and n-pseudo valuation domains |
| 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 and n a positive integer. A proper ideal I of R is an n-semiprimary ideal of R if whenever x^n y^n ∈ I for x, y ∈ R, then x^n ∈ I or y^n ∈ I. Let R be an integral domain with quotient field K. A proper ideal I of R is an n-powerful ideal of R if whenever x^n y^n ∈ I for x, y ∈ K, then x^n ∈ R or y^n ∈ R; and I is an n-powerful semiprimary ideal of R if whenever x^n y^n ∈ I for x, y ∈ K, then x^n ∈ I or y^n ∈ I. If every prime ideal of R is an n-powerful semiprimary ideal of R, then R is an n-pseudo-valuation domain (n-PVD). In this paper, we study the above concepts and relate them to several generalizations of pseudo-valuation domains. |
| format | article |
| id | aus_a0ebcbc3474f0677bb5077e7d9355614 |
| identifier_str_mv | Anderson, D. F., & Badawi, A. (2020). On n-semiprimary ideals and n-pseudo valuation domains. In Communications in Algebra (Vol. 49, Issue 2, pp. 500–520). Informa UK Limited. https://doi.org/10.1080/00927872.2020.1803345 1532-4125 10.1080/00927872.2020.1803345 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/25071 |
| publishDate | 2020 |
| publisher.none.fl_str_mv | Taylor and Francis |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | On n-semiprimary ideals and n-pseudo valuation domainsAnderson, David F.Badawi, AymanPrime ideal2-absorbing idealn-absorbing idealPrimary idealSemiprimary idealRadical idealPowerful idealValuation domainAlmost valuation domainPseudo-valuation domainAlmost pseudo-valuation domainPseudo-almost valuation domainLet R be a commutative ring with 1 ≠ 0 and n a positive integer. A proper ideal I of R is an n-semiprimary ideal of R if whenever x^n y^n ∈ I for x, y ∈ R, then x^n ∈ I or y^n ∈ I. Let R be an integral domain with quotient field K. A proper ideal I of R is an n-powerful ideal of R if whenever x^n y^n ∈ I for x, y ∈ K, then x^n ∈ R or y^n ∈ R; and I is an n-powerful semiprimary ideal of R if whenever x^n y^n ∈ I for x, y ∈ K, then x^n ∈ I or y^n ∈ I. If every prime ideal of R is an n-powerful semiprimary ideal of R, then R is an n-pseudo-valuation domain (n-PVD). In this paper, we study the above concepts and relate them to several generalizations of pseudo-valuation domains.Taylor and Francis2022-11-28T11:44:38Z2022-11-28T11:44:38Z2020-08-14Peer-ReviewedPostprintinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAnderson, D. F., & Badawi, A. (2020). On n-semiprimary ideals and n-pseudo valuation domains. In Communications in Algebra (Vol. 49, Issue 2, pp. 500–520). Informa UK Limited. https://doi.org/10.1080/00927872.2020.18033451532-4125http://hdl.handle.net/11073/2507110.1080/00927872.2020.1803345en_UShttps://doi.org/10.1080/00927872.2020.1803345oai:repository.aus.edu:11073/250712024-08-22T12:02:07Z |
| spellingShingle | On n-semiprimary ideals and n-pseudo valuation domains Anderson, David F. Prime ideal 2-absorbing ideal n-absorbing ideal Primary ideal Semiprimary ideal Radical ideal Powerful ideal Valuation domain Almost valuation domain Pseudo-valuation domain Almost pseudo-valuation domain Pseudo-almost valuation domain |
| status_str | publishedVersion |
| title | On n-semiprimary ideals and n-pseudo valuation domains |
| title_full | On n-semiprimary ideals and n-pseudo valuation domains |
| title_fullStr | On n-semiprimary ideals and n-pseudo valuation domains |
| title_full_unstemmed | On n-semiprimary ideals and n-pseudo valuation domains |
| title_short | On n-semiprimary ideals and n-pseudo valuation domains |
| title_sort | On n-semiprimary ideals and n-pseudo valuation domains |
| topic | Prime ideal 2-absorbing ideal n-absorbing ideal Primary ideal Semiprimary ideal Radical ideal Powerful ideal Valuation domain Almost valuation domain Pseudo-valuation domain Almost pseudo-valuation domain Pseudo-almost valuation domain |
| url | http://hdl.handle.net/11073/25071 |