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

2010/01/04 by Marco D’Anna, D'Anna, Marco, Carmelo Antonio Finocchiaro +3 · 2 citations
Mathematics · #13A15 #13B99 #14A05 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1001.0472

openalex publication_date 2010/01/04 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

Let f:A \→ B be a ring homomorphism and let J be an ideal of B. In\nthis paper, we study the amalgamation of A with B along J with respect to\nf (denoted by A Join^fJ), a construction that provides a general frame\nfor studying the amalgamated duplication of a ring along an ideal, introduced\nand studied by D'Anna and Fontana in 2007, and other classical constructions\n(such as the A+ XB[X], the A+ XB[[X]] and the D+M constructions). In\nparticular, we completely describe the prime spectrum of the amalgamated\nduplication and we give bounds for its Krull dimension.\n

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