On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2
This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal I of a ring R is (1,2)-absorbing primary if, whenever non-unit elements α, β, γ ∈ R with αβγ ∈ I,then αβ ∈ I or γ2 ∈ I. The introduced notion is related to uniformly primary ideals introduced in [5]....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2023-01-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2023-0001 |
| _version_ | 1811159162116112384 |
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| author | Alhazmy Khaled Almahdi Fuad Ali Ahmed Bouba El Mehdi Tamekkante Mohammed |
| author_facet | Alhazmy Khaled Almahdi Fuad Ali Ahmed Bouba El Mehdi Tamekkante Mohammed |
| author_sort | Alhazmy Khaled |
| collection | DOAJ |
| description | This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal I of a ring R is (1,2)-absorbing primary if, whenever non-unit elements α, β, γ ∈ R with αβγ ∈ I,then αβ ∈ I or γ2 ∈ I. The introduced notion is related to uniformly primary ideals introduced in [5]. The first main objective of this paper is to compare (1,2)-absorbing primary ideals with uniformly primary ideals with order less than or equal 2, as well as to characterize them in many classes of rings. The second part of this paper characterizes, by using (1,2)-absorbing primary ideals, the rings R for which all ideals lie between N(R) (the nil-radical of R)and N(R)2. |
| first_indexed | 2024-04-10T05:37:31Z |
| format | Article |
| id | doaj.art-21b3c426949f4983b6ee30424602a373 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-10T05:37:31Z |
| publishDate | 2023-01-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-21b3c426949f4983b6ee30424602a3732023-03-06T17:00:03ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352023-01-0131152110.2478/auom-2023-0001On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2Alhazmy Khaled0Almahdi Fuad Ali Ahmed1Bouba El Mehdi2Tamekkante Mohammed3Department of Mathematics, Faculty of Sciences, King Khalid University, P. O. Box. 9004, Abha, Saudi Arabia.Department of Mathematics, Faculty of Sciences, King Khalid University, P. O. Box. 9004, Abha, Saudi Arabia.Department of Mathematics and computer, Faculty Multidisciplinary of Nador, University Mohammed first, Morocco.Department of Mathematics, Faculty of Science, University Moulay Ismail Box 11201, Zitoune, Meknes, Morocco.This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal I of a ring R is (1,2)-absorbing primary if, whenever non-unit elements α, β, γ ∈ R with αβγ ∈ I,then αβ ∈ I or γ2 ∈ I. The introduced notion is related to uniformly primary ideals introduced in [5]. The first main objective of this paper is to compare (1,2)-absorbing primary ideals with uniformly primary ideals with order less than or equal 2, as well as to characterize them in many classes of rings. The second part of this paper characterizes, by using (1,2)-absorbing primary ideals, the rings R for which all ideals lie between N(R) (the nil-radical of R)and N(R)2.https://doi.org/10.2478/auom-2023-0001(uniformly) primary idealsun-rings1-absorbing primary idealsprimary 13a15secondary 13a99 |
| spellingShingle | Alhazmy Khaled Almahdi Fuad Ali Ahmed Bouba El Mehdi Tamekkante Mohammed On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2 Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica (uniformly) primary ideals un-rings 1-absorbing primary ideals primary 13a15 secondary 13a99 |
| title | On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2 |
| title_full | On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2 |
| title_fullStr | On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2 |
| title_full_unstemmed | On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2 |
| title_short | On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2 |
| title_sort | on 1 2 absorbing primary ideals and uniformly primary ideals with order ≤ 2 |
| topic | (uniformly) primary ideals un-rings 1-absorbing primary ideals primary 13a15 secondary 13a99 |
| url | https://doi.org/10.2478/auom-2023-0001 |
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