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Let $f:A \rightarrow B$ be a ring homomorphism and let $J$ be an ideal of$B$. In this paper, we study the amalgamation of $A$ with $B$ along $J$ withrespect to $f$, a construction that provides a general frame for studying theamalgamated duplication of a ring along an ideal, introduced by D'Anna andFontana in 2007, and other classical constructions (such as the $A+ XB[X]$, the$A+ XB[\![X]\!]$ and the $D+M$ constructions). In particular, we completelydescribe the prime spectrum of the amalgamation and, when it is a localNoetherian ring, we study its embedding dimension and when it turns to be aCohen-Macaulay ring or a Gorenstein ring.

Algebraic and topological properties of an amalgamated algebra along an ideal