相对整体维数有限的扩张

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相对整体维数有限的扩张郭述锋^1,21. 桂林航天工业学院理学院桂林 541004;
2. 首都师范大学数学科学学院北京 100048 Extensions with Finite Relative Global Dimension Shu Feng GUO^1,21. College of Science, Guilin University of Aerospace Technology, Guilin 541004, P. R. China;
2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, P. R. China

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摘要代数的扩张是指两个代数之间保持单位元的同态映射.设f：B→A是代数的扩张，扩张f的相对整体维数是指所有A-模的相对投射维数的上确界.我们给出了扩张的相对整体维数有限的一个充分必要条件，作为应用，还获得了Hochschild的文[Relative homological algebra，Trans.Am.Math.Soc.，1956，82：246–269]中一个结果的简洁证明.

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收稿日期: 2018-04-15

MR (2010):

O154.2

基金资助:国家自然科学基金资助项目（11331006）；广西自然科学基金项目（2018GXNSFAA138191）；桂林航天工业学院博士基金项目（20180601-20200601）

作者简介: 郭述锋,E-mail:guoshufeng132@126.com

引用本文:

郭述锋. 相对整体维数有限的扩张[J]. 数学学报, 2019, 62(2): 191-200. Shu Feng GUO. Extensions with Finite Relative Global Dimension. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 191-200.

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http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2019/V62/I2/191

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