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arXiv · 1312.3804

Algebraic and topological properties of an amalgamated algebra along an ideal

Marco D'Anna·Carmelo Antonio Finocchiaro·Marco Fontana
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Abstract

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 $J$ with respect to $f$, a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced by D'Anna and Fontana in 2007, and other classical constructions (such as the $A+ XB[X]$, the $A+ XB[\![X]\!]$ and the $D+M$ constructions). In particular, we completely describe the prime spectrum of the amalgamation and, when it is a local Noetherian ring, we study its embedding dimension and when it turns to be a Cohen-Macaulay ring or a Gorenstein ring.

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Marco D'Anna, Carmelo Antonio Finocchiaro, Marco Fontana. 2013-12-13. Algebraic and topological properties of an amalgamated algebra along an ideal. https://arxiv.org/abs/1312.3804

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