沿理想 amalgamated 代数的代数与拓扑性质
交换代数
2016-06-23 v3
摘要
设 为环同态， 为 的理想。本文研究了关于 沿 将 与 进行的 amalgamation，该构造为研究 D'Anna 和 Fontana 于 2007 年引入的沿理想的环 amalgamated 倍增以及其他经典构造（如 、 和 构造）提供了一个通用框架。特别地，我们完全描述了该 amalgamation 的素谱，并且当其为局部 Noetherian 环时，研究了其嵌入维数，以及其成为 Cohen-Macaulay 环或 Gorenstein 环的条件。
引用
@article{arxiv.1312.3804,
title = {Algebraic and topological properties of an amalgamated algebra along an ideal},
author = {Marco D'Anna and Carmelo Antonio Finocchiaro and Marco Fontana},
journal= {arXiv preprint arXiv:1312.3804},
year = {2016}
}
备注
The present version of the manuscript differs from the previous one for an appendix where we note that Proposition 4.1(2) and Theorem 4.4 hold under the assumption, not explicitly declared, that B=f(A)+J. In the same appendix, we provide the exact value of ${\rm embdim}(A\Join^fJ)$, under the hypothesis that J is finitely generated as an ideal of the ring f(A)+J. Finally, we deleted Example 4.6