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arXiv · 1001.0472

Properties of chains of prime ideals in an amalgamated algebra along an ideal

Marco D'Anna·Carmelo Finocchiaro·Marco Fontana
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Abstract

Let $f:A \to B$ 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 $f$ (denoted by ${A\Join^fJ}$), a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied 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 amalgamated duplication and we give bounds for its Krull dimension.

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Marco D'Anna, Carmelo Finocchiaro, Marco Fontana. 2010-01-04. Properties of chains of prime ideals in an amalgamated algebra along an ideal. https://arxiv.org/abs/1001.0472

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