Let $f : A ightarrow B$ 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 $A owtie^f J$), 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
Properties of chains of prime ideals in an amalgamated algebra along an ideal
D'ANNA, Marco;FINOCCHIARO C. A;
2010-01-01
Abstract
Let $f : A ightarrow B$ 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 $A owtie^f J$), 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 dimensionFile in questo prodotto:
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