有限扩张环

数学物理学报

有限扩张环

周德旭

福建师范大学数学与计算机科学学院福州 350007

收稿日期:2004-10-12 修回日期:2005-12-12 出版日期:2006-10-25 发布日期:2006-10-25
通讯作者: 周德旭
基金资助:
国家自然科学基金(A0324656),福建省教育厅科技项目A类(JA05212)和福建师范大学青年教师

Finitely Extending Rings

Zhou Dexu

Department of Mathematics, Fujian Normal University, Fuzhou 350007

Received:2004-10-12 Revised:2005-12-12 Online:2006-10-25 Published:2006-10-25
Contact: Zhou Dexu

摘要/Abstract

摘要： 证明了环的有限扩张性可以传递到矩阵环上;通过PP环,半遗传环以及有限余非奇异环刻划了有限扩张环,并推广了文献[2]的定理2.1; 对于FGF与CF猜测,给出了部分肯定的回答,即右有限扩张右CF环是右CEP的,从而是右aritian的,改进了文献[6]的定理3.7.

关键词: n -扩张环, n -余非奇异环, 半遗传环, PP环, QF环

Abstract: Finitely extending property is shown to carry over to matrix rings, and non-singular finitely extending rings are characterized via PP rings, semihereditary rings and finitely co-non-singular rings, these extend [2, Theorem 2.1]; a partial positive answer is provided to the FGF and CF Conjectures, that is, every right finitely extending right CF ring is right CEP (so right aritian), which improve [6, Theorem 3.7].

Key words: n-extending ring, n-co-non-singular ring, Semihereditary ring, PP ring, QF ring

中图分类号:

16D10

周德旭. 有限扩张环[J]. 数学物理学报, 2006, 26(5): 707-715.

Zhou Dexu. Finitely Extending Rings[J]. Acta mathematica scientia,Series A, 2006, 26(5): 707-715.