… Bazzoni conjectured that Prüfer domains for which “an ideal is … is the amalgamated
duplication of a ring along an ideal I (… Then the following conditions are equivalent. (1) Every …

… will use the amalgamated duplication of a ring R along an R-submodule E of the total ring of
… Finally, we end this section by providing an example of a \(\phi \)-Prüfer ring that is not nonnil…

… Also, we introduce the notion of φP -chained rings and we study the … ring between a ring
A and a trivial ring extension A ∝ E (resp., an amalgamated duplication of A along an ideal I). …

… In the following, under certain conditions, we investigate when the zero-divisor graph of …
Let us first introduce the concept of zero-divisor graph for an arbitrary ideal of a ring A. …

… FMR-ring pairs issued from amalgamated duplications of rings and trivial ring extensions. …
section, gives necessary and sufficient conditions for a bi-amalgamation to be an FMR-ring. …

… of the amalgamated duplication of a ring along an ideal (introduced … The interest of
amalgamation resides, partly, in its ability to … conditions under which some trivial extensions of …

… condition “I is a nil ideal of R” in Proposition 2.1 is essential for the converse. Indeed, let A be
any periodic ring… Moutui: Prüfer property in amalgamated algebras along an ideal. Ric. Mat. …

… rings, and we study the possible transfer of this notion to trivial ring extensions and amalgamated
algebras along an ideal. … commutative rings satisfying the above-mentioned properties. …

… the amalgamated algebra (or amalgamation) of R with S along J with respect to f. This
construction generalizes the amalgamated duplication of a ring along an ideal (… the situation in this …

… conditions on a ring such that ωS(R) ⊆ N. In Section 5, the final section of this paper, focuses
on Snabsorbing ideals of the amalgamation of rings… Prüfer domains are locally divided rings…