Lifting units in clean rings

JOURNAL OF ALGEBRA

卷:381

Article

Ster, Janez

关键词: Clean ring;    Lifting units modulo an ideal;    K-theory;    Separativity;    Bergman's example;   

DOI  :  10.1016/j.jalgebra.2013.02.014

来源: Elsevier

【 摘 要 】

Let R be a clean ring with an ideal I such that R/I is semiperfect and K-0(I) is torsion-free. We prove that, under some mild conditions, units in R/I can be lifted to units in R. This implies that the matrix ring M-n(R) over Bergman's example of a non-clean exchange ring R is not clean, for every n. We also obtain some other results concerning lifting units in clean rings: (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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