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

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

2010-01-04

arxiv.org/abs/1001.0472v1

Mathematics

Commutative Algebra

J. Pure Appl. Algebra (to appear)

Scientific paper

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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