Let A and B be commutative rings with identity and J be an ideal of B, and let f: A→ B be a
ring homomorphism. The amalgamation of A with B along J with respect to f denoted by A⋈ f …

Let f WA! B be a ring homomorphism and J an ideal of B. In this paper, we initiate a
systematic study of a new ring construction called the “amalgamation of A with B along J with …

Abstract Let f:A→B and g:A→C be two commutative ring homomorphisms, and let J and J' be
two ideals of B and C, respectively, such that f^-1(J)=g^-1(J'). The bi-amalgamation of A with …

Let f: A→ B, g: A→ C be ring homomorphisms and let 𝔟 (respectively, 𝔠) be an ideal of B
(respectively, C) satisfying f− 1 (𝔟)= g− 1 (𝔠). Recently, Kabbaj, Louartiti and Tamekkante …

Let R be a commutative ring with 1≠0 and let m and n be integers with 1≦n<m. A proper
ideal I of R iscalled an (m,n)-closed ideal of R if whenever a^m∈I forsome a∈R implies …

A NOTE ON AMALGAMATED RINGS ALONG AN IDEAL Marta Nowakowska 1. Introduction
and preliminaries All rings in this paper are associ Page 1 Annales Mathematicae Silesianae …

Let R be a commutative ring with nonzero identity. A proper ideal I of R is called a 1-
absorbing prime ideal (respectively, 1-absorbing primary ideal) if whenever nonunit …

Let R be a commutative ring with nonzero identity. A proper ideal I of R is called a 1-
absorbing prime ideal (respectively, 1-absorbing primary ideal) if whenever nonunit …

Let $ f: A\longrightarrow B $ be a ring homomorphism and let $\mathfrak b $ be an ideal of $
B $. In this paper we study Pr\" ufer like conditions in the amalgamation of $ A $ with $ B …

Abstract Let f: A→ B and g: A→ C be two ring homomorphisms and let J (resp. J′) be an
ideal of B (resp. C) such that f− 1 (J)= g− 1 (J′). We investigate the transfer of the notions of …