New Algebraic Properties of an Amalgamated Algebra Along an Ideal

DOI10.1080/00927872.2015.1033628zbMATH Open1345.13002arXiv1312.3804OpenAlexW2343906631MaRDI QIDQ2813632

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Publication date: 24 June 2016

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Abstract: Let $f:AightarrowB$ 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.

Full work available at URL: https://arxiv.org/abs/1312.3804

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