Let f: A → B be a ring homomorphism, and let J be an ideal of B. In this article, we study the amalgamation of A with B along J with respect to f (denoted by A⋈fJ), 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 A⋈fJ 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.

New Algebraic Properties of an Amalgamated Algebra Along an Ideal

D'ANNA, Marco;Finocchiaro C;
2016-01-01

Abstract

Let f: A → B be a ring homomorphism, and let J be an ideal of B. In this article, we study the amalgamation of A with B along J with respect to f (denoted by A⋈fJ), 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 A⋈fJ 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.
2016
Cohen-Macaulay; Pullback; Zariski topology
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/38070
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