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

By Marco D'anna, C. Finocchiaro, Marco Fontana. 2010

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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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/16541c7bbfc761db72b4b7fce1b97b975da85de9