S.A. Amitsur, Radicals of polynomial rings, Canadian J. Math. 8 (1956), 355–361.
Google Scholar
D.D. Anderson, Commutative rings, in: J.W. Brewer, S. Glaz, W. Heinzer, and B. Olberding (Eds.), Multiplicative Ideal Theory in Commutative Algebra: A Tribute to the Work of Robert Gilmer, Springer, New York, 2006, pp. 1–20.
Google Scholar
T. Anderson, N. Divinsky, and A. Suliński, Hereditary radicals in associative and alternative rings, Canadian J. Math. 17 (1965), 594–603.
Google Scholar
V.A. Andrunakievich, Radicals of associative rings. I, Mat. Sb. (N.S.) 44(86) (1958), 179–212.
Google Scholar
R.R. Andruszkiewicz and M. Kępczyk, On left T-nilpotent rings, Results Math. 79 (2024), no. 4, Paper No. 157, 17 pp.
Google Scholar
W.D. Burgess and R.M. Raphael, Ideal extensions of rings – some topological aspects, Comm. Algebra 23 (1995), no. 10, 3815–3830.
Google Scholar
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.
Google Scholar
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.
Google Scholar
B.S. Chwe and J. Neggers, On the extension of linearly independent subsets of free modules to bases, Proc. Amer. Math. Soc. 24 (1970), 466–470.
Google Scholar
M. D’Anna, A construction of Gorenstein rings, J. Algebra 306 (2006), no. 2, 507–519.
Google Scholar
M. D’Anna, C.A. Finocchiaro, and M. Fontana, Amalgamated algebras along an ideal, in: M. Fontana, S.-E. Kabbaj, B. Olberding, and I. Swanson (Eds.), Commutative Algebra and its Applications, Walter de Gruyter GmbH & Co. KG, Berlin, 2009, pp. 155–172.
Google Scholar
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.
Google Scholar
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.
Google Scholar
J.L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 (1932), no. 2, 85–88.
Google Scholar
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.
Google Scholar
C.J. Everett, An extension theory for rings, Amer. J. Math. 64 (1942), 363–370.
Google Scholar
B.J. Gardner, Some aspects of T-nilpotence, Pacific J. Math. 53 (1974), 117–130.
Google Scholar
B.J. Gardner and R. Wiegandt, Radical theory of rings, Monogr. Textbooks Pure Appl. Math., 261, Marcel Dekker, Inc., New York, 2004.
Google Scholar
S. Kabbaj, K. Louartiti, and M. Tamekkante, Bi-amalgamated algebras along ideals, J. Commut. Algebra 9 (2017), no. 1, 65–87.
Google Scholar
T.Y. Lam, Corner ring theory: a generalization of Peirce decompositions, I, in: A. Facchini, K. Fuller, C.M. Ringel, and C. Santa-Clara (Eds.), Algebras, Rings and Their Representations, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006, pp. 153–182.
Google Scholar
S. Mac Lane, Extensions and obstructions for rings, Illinois J. Math. 2 (1958), 316–345.
Google Scholar
J. Matczuk, Ore extensions over duo rings, J. Algebra 297 (2006), no. 1, 139–154.
Google Scholar
A. Mimouni, Clean-like properties in pullbacks and amalgamation rings, Acta Math. Hungar. 156 (2018), no. 1, 91–101.
Google Scholar
W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269–278.
Google Scholar
W.K. Nicholson and Y. Zhou, Rings in which elements are uniquely the sum of an idempotent and a unit, Glasg. Math. J. 46 (2004), no. 2, 227–236.
Google Scholar
M. Nowakowska, A note on amalgamated rings along an ideal, Ann. Math. Sil. 35 (2021), no. 2, 282–288.
Google Scholar
M. Petrich, Ideal extensions of rings, Acta Math. Hungar. 45 (1985), no. 3–4, 263–283.
Google Scholar
J. Szendrei, On the Jacobson radical of a ring, Publ. Math. Debrecen 4 (1955), 93–97.
Google Scholar