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Original Articles

Trivial Extensions Defined by Coherent-like Conditions

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Pages 3937-3953 | Received 01 Apr 2003, Published online: 24 Jun 2011

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (20)

Mohamed Chhiti & Salah Eddine Mahdou. (2023) When every regular ideal is S-finite. Quaestiones Mathematicae 0:0, pages 1-12.
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Najib Mahdou, Abdeslam Mimouni & Youssef Zahir. (2023) On S-1-absorbing prime and weakly S-1-absorbing prime ideals. Quaestiones Mathematicae 46:1, pages 101-115.
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Adam Anebri, Najib Mahdou & Ünsal Tekir. (2022) On modules satisfying the descending chain condition on r-submodules. Communications in Algebra 50:1, pages 383-391.
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Chahrazade Bakkari, Najib Mahdou & Abdelkbir Riffi. (2021) Uniformly graded-coherent rings. Quaestiones Mathematicae 44:10, pages 1371-1391.
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Abdelhaq El Khalfi, Mohammed Issoual, Najib Mahdou & Andreas Reinhart. (2021) Commutative rings with one-absorbing factorization. Communications in Algebra 49:6, pages 2689-2703.
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Abdelhaq El Khalfi, Najib Mahdou & Youssef Zahir. (2021) Strongly primary ideals in rings with zero-divisors. Quaestiones Mathematicae 44:5, pages 569-580.
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Najib Mahdou, Sanae Moussaoui & Siamak Yassemi. (2021) The divided, going-down, and Gaussian properties of amalgamation of rings. Communications in Algebra 49:5, pages 1938-1949.
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Abdelhaq El Khalfi, Hwankoo Kim & Najib Mahdou. (2021) On -piecewise Noetherian rings. Communications in Algebra 49:3, pages 1324-1337.
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K. Adarbeh & S. Kabbaj. (2020) Trivial extensions subject to semi-regularity and semi-coherence. Quaestiones Mathematicae 43:1, pages 45-54.
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David E. Dobbs, Abdelhaq El Khalfi & Najib Mahdou. (2019) Trivial extensions satisfying certain valuation-like properties. Communications in Algebra 47:5, pages 2060-2077.
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François Couchot. (2015) Gaussian Trivial Ring Extensions and FQP-rings. Communications in Algebra 43:7, pages 2863-2874.
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Najib Mahdou & Hakima Mouanis. (2015) On Steinitz-like conditions. Journal of Taibah University for Science 9:3, pages 340-345.
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Najib Mahdou & Mohammed Zennayi. (2015) On adequate rings. Journal of Taibah University for Science 9:3, pages 320-325.
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Najib Mahdou, Abdeslam Mimouni & Moutu Abdou Salam Moutui. (2015) On Almost Valuation and Almost Bézout Rings. Communications in Algebra 43:1, pages 297-308.
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M. Chhiti, M. Jarrar, S. Kabbaj & N. Mahdou. (2015) Prüfer Conditions in an Amalgamated Duplication of a Ring Along an Ideal. Communications in Algebra 43:1, pages 249-261.
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Mohammed Kabbour & Najib Mahdou. (2010) On Valuation Rings. Communications in Algebra 39:1, pages 176-183.
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Driss Bennis. (2009) Rings Over Which the Class of Gorenstein Flat Modules is Closed Under Extensions. Communications in Algebra 37:3, pages 855-868.
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Chahrazade Bakkari, Najib Mahdou & Hakima Mouanis. (2009) Prüfer-Like Conditions in Subring Retracts and Applications. Communications in Algebra 37:1, pages 47-55.
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DavidE. Dobbs. (2006) Every Commutative Ring Has a Minimal Ring Extension. Communications in Algebra 34:10, pages 3875-3881.
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Chahrazade Bakkari & Najib Mahdou. (2006) Gaussian Polynomials and Content Ideal in Pullbacks. Communications in Algebra 34:8, pages 2727-2732.
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Articles from other publishers (57)

Adam Anebri, Abdelhaq El Khalfi & Najib Mahdou. (2022) On (1,r)-ideals of commutative rings. Journal of Algebra and Its Applications 23:02.
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Najib Mahdou, Suat Koç, Eda Yıldız & Ünsal Tekir. (2023) Annihilator Condition on Modules. Iranian Journal of Science 47:5-6, pages 1713-1721.
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Haitham El Alaoui & Mourad El Maalmi. (2023) Amalgamations subject to weakly finite conductor and P-coherence. São Paulo Journal of Mathematical Sciences 17:2, pages 902-913.
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Ayman Badawi, Abdelhaq El Khalfi & Najib Mahdou. (2023) On (m, n)-absorbing prime ideals and (m, n)-absorbing ideals of commutative rings. São Paulo Journal of Mathematical Sciences 17:2, pages 888-901.
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Abdeslam Mimouni. (2022) Ideal containment in commutative rings. Journal of Algebra and Its Applications 22:09.
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S. Kabbaj & A. Mimouni. (2022) Reductions and cores of ideals in trivial ring extensions. Journal of Algebra and Its Applications 22:07.
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Hwankoo KIM, Najib MAHDOU & El Houssaine OUBOUHOU. (2023) When every ideal is $\phi$-P-flat. Hacettepe Journal of Mathematics and Statistics 52:3, pages 708-720.
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Oussama Aymane Es SAFI, Najib MAHDOU & Mohamed YOUSIF. (2023) Rings with divisibility on ascending chains of ideals. International Electronic Journal of Algebra, pages 1-8.
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Junpeng Wang & Xiaoxiang Zhang. (2022) On rings with finite Gorenstein weak global dimension. Journal of Algebra and Its Applications 22:05.
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Moutu Abdou Salam Moutui, Najib Ouled Azaiez & Suat Koç. (2023) Classes of trivial ring extensions and amalgamations subject to pseudo-almost valuation condition. Georgian Mathematical Journal 0:0.
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Haitham El Alaoui & Hakima Mouanis. (2022) On weak P-coherent rings. Asian-European Journal of Mathematics 16:01.
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Rachida El Khalfaoui, Najib Mahdou & Siamak Yassemi. (2021) Local dimension of trivial extension and amalgamation of rings. Journal of Algebra and Its Applications 22:01.
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Najib Mahdou & Sanae Moussaoui. (2022) About weak $\pi$-rings. Boletim da Sociedade Paranaense de Matemática 41, pages 1-8.
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Samir Bouchiba & Salah Kabbaj. (2022) ON THE FINITENESS OF EXT-INDICES OF RING EXTENSIONS. Rocky Mountain Journal of Mathematics 52:6.
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Eugenia Ellis & Rafael Parra. (2021) K-theory of n-coherent rings. Journal of Algebra and Its Applications 21:12.
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Ahmad Yousefian Darani, Najib Mahdou & Sanae Moussaoui. (2021) Strongly ϕ-n-irreducible ideals. Journal of Algebra and Its Applications 21:12.
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A. Mimouni. (2022) Nil-ideals, J-ideals and their generalizations in commutative rings. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry.
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Anass Assarrar, Najib Mahdou, Ünsal Tekir & Suat Koç. (2022) On graded coherent-like properties in trivial ring extensions. Bollettino dell'Unione Matematica Italiana 15:3, pages 437-449.
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Najib Mahdou, Sanae Moussaoui & Moutu Abdou Salam Moutui. (2021) When every finitely projective ideal is projective. Indian Journal of Pure and Applied Mathematics 53:3, pages 579-586.
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Malik Tusif Ahmed, Najib Mahdou & Youssef Zahir. (2021) Commutative rings with invertible-radical factorization. Journal of Algebra and Its Applications 21:08.
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Najib Mahdou, Moutu Abdou Salam Moutui & Youssef Zahir. (2022) On 𝑆-weakly prime ideals of commutative rings. Georgian Mathematical Journal 29:3, pages 397-405.
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Mohammed ISSOUAL, Najib MAHDOU & Moutu ABDOU SALAM MOUTUİ. (2022) On $n$-absorbing prime ideals of commutative rings. Hacettepe Journal of Mathematics and Statistics 51:2, pages 455-465.
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Haitham El Alaoui & Hakima Mouanis. (2022) About weakly Bézout rings. Boletim da Sociedade Paranaense de Matemática 40, pages 1-6.
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Ali BenhissiAli Benhissi. 2022. Chain Conditions in Commutative Rings. Chain Conditions in Commutative Rings 1 109 .
Abdelhaq El KhalfiNajib MahdouÜnsal TekirSuat Koç. (2021) On 1-absorbing δ -primary ideals . Analele Universitatii "Ovidius" Constanta - Seria Matematica 29:3, pages 135-150.
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Abdelhaq El Khalfi, Hwankoo Kim & Najib Mahdou. (2020) Amalgamated Algebras Issued from $$\phi $$-Chained Rings and $$\phi $$-Pseudo-Valuation Rings. Bulletin of the Iranian Mathematical Society 47:5, pages 1599-1609.
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Mohamed Issoual. (2020) Rings in which every 2-absorbing primary ideal is primary. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 62:3, pages 605-614.
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Tiberiu Dumitrescu, Najib Mahdou & Youssef Zahir. (2020) Radical factorization for trivial extensions and amalgamated duplication rings. Journal of Algebra and Its Applications 20:02, pages 2150025.
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Abdelhaq El Khalfi, Najib Mahdou & Youssef Zahir. (2020) Rings in which every nonzero weakly prime ideal is prime. São Paulo Journal of Mathematical Sciences 14:2, pages 689-697.
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Abdelhaq El Khalfi & Najib Mahdou. (2019) Almost Bézout rings and almost GCD-rings. Asian-European Journal of Mathematics 13:06, pages 2050107.
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Rachida El Khalfaoui & Najib Mahdou. (2020) On stable range one property and strongly $$\pi $$-regular rings. Afrika Matematika 31:5-6, pages 1047-1056.
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Weiqing Li & Dong Liu. (2019) A non-commutative analogue of Costa’s first conjecture. Journal of Algebra and Its Applications 19:01, pages 2050007.
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Mohamed Issoual & Najib Mahdou. 2020. Differential Geometry, Algebra, and Analysis. Differential Geometry, Algebra, and Analysis 147 155 .
Najib Mahdou & Rachida El Khalfaoui. (2019) Commutative rings in which every pure ideal is projective. ANNALI DELL'UNIVERSITA' DI FERRARA 65:2, pages 301-310.
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Rachida El Khalfaoui & Najib Mahdou. (2019) Rings in which every regular locally principal ideal is projective. Studia Scientiarum Mathematicarum Hungarica 56:2, pages 241-251.
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Mounir El Ouarrachi & Najib Mahdou. (2018) Power Serieswise Armendariz Property in Amalgamated Algebra. Bulletin of the Iranian Mathematical Society 45:1, pages 23-33.
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Mohammed Issoual & Najib Mahdou. (2018) Trivial extensions defined by 2-absorbing-like conditions. Journal of Algebra and Its Applications 17:11, pages 1850208.
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Mounir El Ouarrachi & Najib Mahdou. 2018. Homological and Combinatorial Methods in Algebra. Homological and Combinatorial Methods in Algebra 127 138 .
Haitham El Alaoui. 2018. Homological and Combinatorial Methods in Algebra. Homological and Combinatorial Methods in Algebra 117 126 .
Karima Alaoui Ismaili, David E. Dobbs & Najib Mahdou. (2017) Commutative rings and modules that are Nil*-coherent or special Nil*-coherent. Journal of Algebra and Its Applications 16:10, pages 1750187.
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Najib Mahdou & Mohammed Zennayi. (2017) On Henriksen rings. Journal of Algebra and Its Applications 16:03, pages 1750058.
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K. Adarbeh & S. Kabbaj. (2016) Zaks' conjecture on rings with semi-regular proper homomorphic images. Journal of Algebra 466, pages 169-183.
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Karima Alaoui Ismaili & Najib Mahdou. (2016) On (n,d)-property in amalgamated algebra. Asian-European Journal of Mathematics 09:01, pages 1650014.
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Jiangsheng Hu, Haiyu Liu & Yuxian Geng. (2015) When every pure ideal is projective. Journal of Algebra and Its Applications 15:02, pages 1650030.
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F. Cheniour & N. Mahdou. (2015) On some flatness properties over commutative rings. Acta Mathematica Hungarica 146:1, pages 142-152.
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Chahrazade Bakkari & Najib Mahdou. (2014) On weakly coherent rings. Rocky Mountain Journal of Mathematics 44:3.
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Khalid Adarbeh & Salah-Eddine Kabbaj. 2014. Commutative Algebra. Commutative Algebra 1 23 .
Fatima Cheniour & Najib Mahdou. (2013) When every flat ideal is finitely projective. Arabian Journal of Mathematics 2:3, pages 255-261.
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Najib Mahdou & Khalid Ouarghi. (2012) On G-$(n,d)$-rings. Rocky Mountain Journal of Mathematics 42:3.
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Najib Mahdou & Aziza Rahmouni Hassani. (2010) On Strong (A)-Rings. Mediterranean Journal of Mathematics 9:2, pages 393-402.
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S. El Baghdadi, A. Jhilal & N. Mahdou. (2012) On FF-rings. Journal of Pure and Applied Algebra 216:1, pages 71-76.
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J. Abuhlail, M. Jarrar & S. Kabbaj. (2011) Commutative rings in which every finitely generated ideal is quasi-projective. Journal of Pure and Applied Algebra 215:10, pages 2504-2511.
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Marco D’Anna, Carmelo A. Finocchiaro & Marco Fontana. (2010) Properties of chains of prime ideals in an amalgamated algebra along an ideal. Journal of Pure and Applied Algebra 214:9, pages 1633-1641.
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C. Bakkari, S. Kabbaj & N. Mahdou. (2010) Trivial extensions defined by Prüfer conditions. Journal of Pure and Applied Algebra 214:1, pages 53-60.
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Chahrazade Bakkari. (2009) Armendariz and SFT Properties in Subring Retracts. Mediterranean Journal of Mathematics 6:3, pages 339-345.
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D. D. Anderson & M. Winders. (2009) Idealization of a Module. Journal of Commutative Algebra 1:1.
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Najib Mahdou. (2006) On -flat modules and -Von Neumann regular rings . International Journal of Mathematics and Mathematical Sciences 2006, pages 1-6.
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