References
- [1] D.D. Anderson, Commutative rings, in: J.W. Brewer et al. (Eds.), Multiplicative Ideal Theory in Commutative Algebra. A Tribute to the Work of Robert Gilmer, Springer, New York, 2006, pp. 1–20.10.1007/978-0-387-36717-0_1
- [2] M. Chhiti and N. Mahdou, Some homological properties of amalgamated duplication of a ring along an ideal, Bull. Iranian Math. Soc. 38 2012, no. 2, 507–515.
- [3] M. Chhiti, N. Mahdou, and M. Tamekkante, Clean property in amalgamated algebras along an ideal, Hacet. J. Math. Stat. 44 2015, no. 1, 41–49.
- [4] M. D’Anna, A construction of Gorenstein rings, J. Algebra 306 2006, no. 2, 507–519.10.1016/j.jalgebra.2005.12.023
- [5] M. D’Anna, C.A. Finocchiaro, and M. Fontana, Amalgamated algebras along an ideal, in: M. Fontana et al. (Eds.), Commutative Algebra and its Applications, Walter de Gruyter, Berlin, 2009, pp. 155–172.10.1515/9783110213188.155
- [6] M. D’Anna, C.A. Finocchiaro, and M. Fontana, Properties of chains of prime ideals in amalgamated algebra along an ideal, J. Pure Appl. Algebra 214 2010, no. 9, 1633–1641.10.1016/j.jpaa.2009.12.008
- [7] M. D’Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic propeties, J. Algebra Appl. 6 2007, no. 3, 443–459.10.1142/S0219498807002326
- [8] J.L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 1932, no. 2, 85–88.10.1090/S0002-9904-1932-05333-2
- [9] M. El Maalmi and H. Mouanis, On Steinitz-like properties in amalgamated algebras along an ideal, J. Algebra Appl. 19 2020, no. 12, 2050237, 9 pp.10.1142/S0219498820502370
- [10] B.J. Gardner and R. Wiegandt, Radical Theory of Rings, Monographs and Textbooks in Pure and Applied Mathematics, 261, Marcel Dekker, Inc., New York, 2004.
- [11] S. Kabbaj, K. Louariti, and M. Tamekkante, Bi-amalgamated algebras along ideals, J. Commut. Algebra 9 2017, no. 1, 65–87.10.1216/JCA-2017-9-1-65
- [12] H. Kose, Y. Kurtulmaz, B. Ungor, and A. Harmanci, Semicommutativity of amalgamated rings, J. Math. Res. Appl. 38 2018, no. 4, 366–376.
- [13] A. Mimouni, Clean-like properties in pullbacks and amalgamation rings, Acta Math. Hungar. 156 2018, no. 1, 91–101.10.1007/s10474-018-0859-y
- [14] M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, 13, Interscience Publishers a division of John Wiley & Sons, New York, 1962.