Strong Separativity over Regular Rings

• 作者: Huanyin Chen
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 正则环 可分性 有限生成 强分离 理想环 单位 R-模
• 年，卷（期）: 2015,（3）
• 页码范围: 413-420
• 页数: 8页
• 分类号: O153.3
• 语种: 中文

摘要

An ideal I of a ring R is strongly separative provided that for all finitely generated projective R-modules A, B with A = AI and B = BI, if 2A ≌ A + B, then A ≌ B. We prove in this paper that a regular ideal I of a ring R is strongly separative if and only if each a E 1 + I satisfying (1 - α)R ∝ r(a) is unit-regular, if and only if each a ∈ 1 + I satisfying (1 - a2)R ∝ r(a2) is unit-regular, if and only if each a E 1 4- I satisfying R(1 - a)R = Rr(a) is unit-regular, if and only if each a ∈ 1 + I satisfying R(1 -a^2)R = Rr(a^2) is unit-regular.