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

Let R and S be commutative rings with identity, J be an ideal of S, f: R→ S be a ring
homomorphism, M be an R-module, N be an S-module, and let φ: M→ N be an R …

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 R be a commutative ring and let I be a nonzero proper ideal of R. In this paper, we study
the properties of a family of rings R (I) a, b, with a, b∈ R, as quotients of the Rees algebra⊕ …

Let R be a commutative Noetherian ring and let I≠ 0 be a proper ideal of R. We study some
properties of a family of rings R (I) a, b that are obtained as quotients of the Rees algebra …

Let R be a commutative ring and let I≠ 0 be a proper ideal of R. In this paper, we study
some algebraic and homological properties of a family of rings R (I) a, b, with a, b∈ R, that …