research

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

Abstract

Let f:A→Bf:A \to B be a ring homomorphism and let JJ be an ideal of BB. In this paper, we study the amalgamation of AA with BB along JJ with respect to ff (denoted by A⋈fJ{A\Join^fJ}), 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]A+ XB[X], the A+XB[[X]]A+ XB[[X]] and the D+MD+M constructions). In particular, we completely describe the prime spectrum of the amalgamated duplication and we give bounds for its Krull dimension.Comment: J. Pure Appl. Algebra (to appear

    Similar works