On the Stable Rank of Localizations of Affine Algebras

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: stable rank affine algebra primary decomposition
• 年，卷（期）: 2001,（3）
• 页码范围: 241-248
• 页数: 8页
• 分类号: O1
• 语种: 英文

摘要

Let k be an uncountable field. We show that for any finitely generated k-algebra A and integers n, d such that 1 ≤ n ≤ d+ 1 ≤ dimA+ 1, there exists a localization R = S-1A such that dim R = dim A, dim Max(R) = d, and sr(R) = n.Also, we prove that if A is a local domain of geometric origin with dimA ≥ 3,then there is 0 ≠π∈ A such that sr(Aπ) ≥ 2.