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

DOI10.1016/J.JPAA.2009.12.008zbMATH Open1191.13006arXiv1001.0472OpenAlexW2963052296MaRDI QIDQ964519

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Publication date: 22 April 2010

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Abstract: Let $f:AoB$ 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 $AJoi{n}^{f}J$), 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.

Full work available at URL: https://arxiv.org/abs/1001.0472

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