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

被引：144

作者：

D'Anna, Marco ^{[1
]}

Finocchiaro, Carmelo A. ^{[2
]}

Fontana, Marco ^{[2
]}

机构：

[1] Univ Catania, Dipartimento Matemat & Informat, Catania, Italy

[2] Univ Roma Tre, Dipartimento Matemat, Rome, Italy

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2010年 / 214卷 / 09期

关键词：

GORENSTEIN RINGS; INTEGRAL-DOMAINS; DUPLICATION; EXTENSIONS;

D O I：

10.1016/j.jpaa.2009.12.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f : A -> 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 infinity(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. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：1633 / 1641

页数：9

共 21 条

[11] On the prime spectrum, Krull dimension and catenarity of integral domains of the form A plus XB[[X]] [J].