Let f: A→ B be a ring homomorphism, and let J be an ideal of B. In this article, we study the
amalgamation of A with B along J with respect to f (denoted by A⋈ f J), a construction that …

Let A⊆ B be a commutative ring extension such that B is a trivial extension of A (denoted by
A∝ E) or an amalgamated duplication of A along some ideal of A (denoted by A⋈ I). This …

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\rightarrow B $ be a ring homomorphism and let $ J $ be an ideal of $ B $. In this
paper, we investigate the transfert of the property of coherence to the amalgamation …

Let A be a commutative ring and I an ideal of A. The amalgamated duplication of A along I,
denoted by A ⋈ IA⋈ I, is the special subring of A * AA× A defined by A ⋈ I:= π AI π={(a, a+ i) …

This paper establishes necessary and sufficient conditions for a bi-amalgamation to inherit
the S-Noetherian property. The new results compare to previous works carried on various …

arXiv:0903.2240v1 [math.AC] 12 Mar 2009 Some homological properties of an amalgamated
duplication of a ring along an ideal Page 1 arXiv:0903.2240v1 [math.AC] 12 Mar 2009 Some …

Let $ R $ be a commutative ring with identity. A proper ideal $ P $ is said to be weakly prime
ideal of $ R $ if for every $0\neq ab\in P $ where $ a, b\in R, $ implies $ a\in P $ or $ b\in P …

A ring R has the (A)-property (resp., strong (A)-property) if every finitely generated ideal of R
consisting entirely of zero divisors (resp., every finitely generated ideal of R generated by a …

In this paper we improve the recent results on the transfer of Pr\" ufer, Gaussian and
arithmetical conditions on amalgamated constructions. As an application we provide an …