On 2r-ideals in commutative rings with zero-divisors
In this article, we are interested in uniformly prpr-ideals with order ≤2\le 2 (which we call 2r2r-ideals) introduced by Rabia Üregen in [On uniformly pr-ideals in commutative rings, Turkish J. Math. 43 (2019), no. 4, 18781886]. Several characterizations and properties of these ideals are given. Mor...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-06-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0576 |
| _version_ | 1797806241082245120 |
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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 | In this article, we are interested in uniformly prpr-ideals with order ≤2\le 2 (which we call 2r2r-ideals) introduced by Rabia Üregen in [On uniformly pr-ideals in commutative rings, Turkish J. Math. 43 (2019), no. 4, 18781886]. Several characterizations and properties of these ideals are given. Moreover, the comparison between the (nonzero) 2r2r-ideals and certain classes of classical ideals gives rise to characterizations of certain rings based only on the properties of the ideals consisting only of zero-divisors. Namely, among other things, we compare the class of (nonzero) 2r2r-ideals with the class of (minimal) prime ideals, the class of minimal prime ideals and their squares, and the class of primary ideals. The study of 2r2r-ideal in polynomial rings allows us to give a new characterization of the rings satisfying the famous AA-property. |
| first_indexed | 2024-03-13T06:04:18Z |
| format | Article |
| id | doaj.art-749f596d0da64af8a2a53d775d7bae7b |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-03-13T06:04:18Z |
| publishDate | 2023-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-749f596d0da64af8a2a53d775d7bae7b2023-06-12T06:31:09ZengDe GruyterOpen Mathematics2391-54552023-06-012111061107310.1515/math-2022-0576On 2r-ideals in commutative rings with zero-divisorsAlhazmy Khaled0Almahdi Fuad Ali Ahmed1Bouba El Mehdi2Tamekkante Mohammed3Department of Mathematics, Faculty of Sciences, King Khalid University, P. O. Box. 9004, Abha, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, King Khalid University, P. O. Box. 9004, Abha, Saudi ArabiaDepartment of Mathematics and Computer, Faculty Multidisciplinary of Nador, University Mohammed first, Nador, MoroccoDepartment of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Box 11201, Zitoune, MoroccoIn this article, we are interested in uniformly prpr-ideals with order ≤2\le 2 (which we call 2r2r-ideals) introduced by Rabia Üregen in [On uniformly pr-ideals in commutative rings, Turkish J. Math. 43 (2019), no. 4, 18781886]. Several characterizations and properties of these ideals are given. Moreover, the comparison between the (nonzero) 2r2r-ideals and certain classes of classical ideals gives rise to characterizations of certain rings based only on the properties of the ideals consisting only of zero-divisors. Namely, among other things, we compare the class of (nonzero) 2r2r-ideals with the class of (minimal) prime ideals, the class of minimal prime ideals and their squares, and the class of primary ideals. The study of 2r2r-ideal in polynomial rings allows us to give a new characterization of the rings satisfying the famous AA-property.https://doi.org/10.1515/math-2022-0576uniformly pr-idealszero-divisorsa-property13a1513e0513f20 |
| spellingShingle | Alhazmy Khaled Almahdi Fuad Ali Ahmed Bouba El Mehdi Tamekkante Mohammed On 2r-ideals in commutative rings with zero-divisors Open Mathematics uniformly pr-ideals zero-divisors a-property 13a15 13e05 13f20 |
| title | On 2r-ideals in commutative rings with zero-divisors |
| title_full | On 2r-ideals in commutative rings with zero-divisors |
| title_fullStr | On 2r-ideals in commutative rings with zero-divisors |
| title_full_unstemmed | On 2r-ideals in commutative rings with zero-divisors |
| title_short | On 2r-ideals in commutative rings with zero-divisors |
| title_sort | on 2r ideals in commutative rings with zero divisors |
| topic | uniformly pr-ideals zero-divisors a-property 13a15 13e05 13f20 |
| url | https://doi.org/10.1515/math-2022-0576 |
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