References
- D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra 1 (2009), no. 1, 3-56. https://doi.org/10.1216/JCA-2009-1-1-3
- C. Bakkari, S.-E. Kabbaj, and N. Mahdou, Trivial extensions defined by Prufer conditions, J. Pure Appl. Algebra 214 (2010), no. 1, 53-60. https://doi.org/10.1016/j.jpaa.2009.04.011
- M. D'Anna, A construction of Gorenstein rings, J. Algebra 306 (2006), no. 2, 507-519. https://doi.org/10.1016/j.jalgebra.2005.12.023
- M. D'Anna, C. A. Finocchiaro, and M. Fontana, Amalgamated algebras along an ideal, in Commutative algebra and its applications, 155-172, Walter de Gruyter, Berlin, 2009.
- M. D'Anna, C. A. Finocchiaro, and M. Fontana, Properties of chains of prime ideals in an amalgamated algebra along an ideal, J. Pure Appl. Algebra 214 (2010), no. 9, 1633-1641. https://doi.org/10.1016/j.jpaa.2009.12.008
- M. D'Anna and M. Fontana, The amalgamated duplication of a ring along a multiplicative-canonical ideal, Ark. Mat. 45 (2007), no. 2, 241-252. https://doi.org/10.1007/s11512-006-0038-1
- M. D'Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, J. Algebra Appl. 6 (2007), no. 3, 443-459. https://doi.org/10.1142/S0219498807002326
- D. E. Dobbs, A. El Khalfi, and N. Mahdou, Trivial extensions satisfying certain valuation-like properties, Comm. Algebra 47 (2019), no. 5, 2060-2077. https://doi.org/10.1080/00927872.2018.1527926
- T. Dumitrescu, N. Mahdou, and Y. Zahir, Radical factorization for trivial extensions and amalgamated duplication rings, J. Algebra Appl. 20 (2021), no. 2, Paper No. 2150025, 10 pp. https://doi.org/10.1142/S0219498821500250
- A. El Khalfi, H. Kim, and N. Mahdou, Amalgamation extension in commutative ring theory: a survey, Moroccan J. Alg. Geom. Appl. 1 (2022), no. 1, 139-182.
- C. A. Finocchiaro, Amalgamation of algebras and the ultrafilter topology on the Zariski space of valuation overrings of an integral domain, PhD Thesis, University Roma Tre, 2010.
- S. Glaz, Commutative coherent rings, Lecture Notes in Mathematics, 1371, Springer, Berlin, 1989. https://doi.org/10.1007/BFb0084570
- J. A. Huckaba, Commutative rings with zero divisors, Monographs and Textbooks in Pure and Applied Mathematics, 117, Marcel Dekker, Inc., New York, 1988.
- K. A. Ismaili, D. E. Dobbs, and N. Mahdou, Commutative rings and modules that are Nil∗-coherent or special Nil∗-coherent, J. Algebra Appl. 16 (2017), no. 10, 1750187, 24 pp. https://doi.org/10.1142/S0219498817501870
- K. A. Ismaili and N. Mahdou, Coherence in amalgamated algebra along an ideal, Bull. Iranian Math. Soc. 41 (2015), no. 3, 625-632. https://doi.org/10.1016/j.jtusci.2015.02.006
- M. Issoual and N. Mahdou, Trivial extensions defined by 2-absorbing-like conditions, J. Algebra Appl. 17 (2018), no. 11, 1850208, 10 pp. https://doi.org/10.1142/S0219498818502080
- M. Issoual, N. Mahdou, and M. A. S. Moutui, On n-absorbing and strongly n-absorbing ideals of amalgamation, J. Algebra Appl. 19 (2020), no. 10, 2050199, 16 pp. https://doi.org/10.1142/S0219498820501996
- M. Issoual, N. Mahdou, and M. A. S. Moutui, On (m, n)-closed ideals in amalgamated algebra, Int. Electron. J. Algebra 29 (2021), 134-147. https://doi.org/10.24330/ieja.852120
- S.-E. Kabbaj and N. Mahdou, Trivial extensions of local rings and a conjecture of Costa, in Commutative ring theory and applications (Fez, 2001), 301-311, Lecture Notes in Pure and Appl. Math., 231, Dekker, New York, 2003.
- S.-E. Kabbaj and N. Mahdou, Trivial extensions defined by coherent-like conditions, Comm. Algebra 32 (2004), no. 10, 3937-3953. https://doi.org/10.1081/AGB200027791
- N. Mahdou, On Costa's conjecture, Comm. Algebra 29 (2001), no. 7, 2775-2785. https://doi.org/10.1081/AGB-100104986
- N. Mahdou, On 2-von Neumann regular rings, Comm. Algebra 33 (2005), no. 10, 3489- 3496. https://doi.org/10.1080/00927870500242991
- N. Mahdou, S. Moussaoui, and S. Yassemi, The divided, going-down, and Gaussian properties of amalgamation of rings, Comm. Algebra 49 (2021), no. 5, 1938-1949. https://doi.org/10.1080/00927872.2020.1859523
- N. Mahdou and M. A. S. Moutui, Gaussian and Prufer conditions in bi-amalgamated algebras, Czechoslovak Math. J. 70(145) (2020), no. 2, 381-391. https://doi.org/10.21136/CMJ.2019.0335-18
- N. Mahdou and M. A. S. Moutui, Prufer property in amalgamated algebras along an ideal, Ric. Mat. 69 (2020), no. 1, 111-120. https://doi.org/10.1007/s11587-019-00451-1
- A. Mimouni, M. Kabbour, and N. Mahdou, Trivial ring extensions defined by arithmetical-like properties, Comm. Algebra 41 (2013), no. 12, 4534-4548. https://doi.org/10.1080/00927872.2012.705932