… transfer of Prüfer conditions between a ring and its total ring of … of the notions of local Prüfer
ring and total ring of quotients. … , fqp conditions to amalgamated duplication along an ideal. At …

… Let f : A → B and g: A → C be two ring homomorphisms and let J and J′ be ideals of B and
… the notions of Gaussian and Prüfer rings to the bi-amalgamation of A with (B,C) along (J, J′) …

… characterizes when an amalgamation of rings is a φ-rings and we … -Prüfer in the amalgamation
algebra along an ideal. Recall from [2] that a ring R is called φ-Prüfer if R/Nil(R) is a Prüfer …

… We show first that every ideal of B is homogeneous by verifying condition (5) in [3, … and
amalgamated duplication Recall that a Prüfer ring is a ring whose finitely generated regular ideals …

… 4 we investigate the problem of when the ring A ⊳⊲f,g (b, c) is Prüfer. A precise answer is
given in … 5 we provide conditions for a bi-amalgamation to be a Gauss ring and new examples. …

… and sufficient conditions for the amalgamated algebra A ⋈ f J … the amalgamated duplication
of a ring along an ideal and the … if R ⋈ I is a Prüfer ring, then R is a Prüfer ring and I m = r I m …

… The amalgamation of A with B along J with respect to f … of the amalgamated duplication of a
ring along an ideal introduced by … conditions that make an integral domain A a Prüfer domain, …

… properties to amalgamated duplication along an ideal with … and original examples of rings
satisfying the above properties. … , Prüfer conditions in an amalgamated duplication of a ring …

… ′ of R is a Prüfer domain with torsion class group and R ⊆ R … In this paper, we examine
when a bi-amalgamation is an AB−ring. Our results capitalize previous well known results on …

… ideal, grade primary ideal amalgamated and we show that if I is a graded ideal of A, then \(I\bowtie
^f J\) is a graded ideal … We show also that I is a graded primary ideal of A if and only if \(…