关于环的Q-clean性及Q-clean corner的讨论

doi:10.6040/j.issn.1671-9352.0.2018.633

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (2): 79-83.doi: 10.6040/j.issn.1671-9352.0.2018.633

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关于环的Q-clean性及Q-clean corner的讨论

孙晓青¹,肖燕婷¹,崔冉冉²

1.西安理工大学理学院, 陕西西安 710054;2.河南工业大学理学院, 河南郑州 450001

发布日期:2020-02-14
作者简介:孙晓青(1984— ),女,博士,副教授,研究方向为代数学. E-mail:sunxq102@163.com
基金资助:
国家自然科学基金资助项目(11601419);河南省自然科学基金研究项目(162300410066)

Discussions on the Q-cleanness of rings and Q-clean corner

SUN Xiao-qing¹, XIAO Yan-ting¹, CUI ran-ran ²

1. School of Science, Xian University of Technology, Xian 710054, Shaanxi, China;
2. College of Science, Henan University of Technology, Zhengzhou 450001, Henan, China

Published:2020-02-14

摘要/Abstract

摘要： 利用拟逆元,定义了Q-clean环和Q-clean corner,研究了环的Q-clean性及Q-clean corner,得到了abelian Q-clean的等价条件,此外一些结论对应到Clean环上也是成立的。

关键词: 拟逆元, Clean环, corner

Abstract: The concepts of Q-clean rings and Q-clean corners are defined by quasi-inverse elements. The Q-cleanness and Q-clean corners of rings are introduced, and some equivalent conditions of abelian Q-clean correspond are given. Moreover, some conclusions can correspond to Clean rings.

Key words: quasi-invertible element, clean ring, corner

中图分类号:

O153.3

孙晓青,肖燕婷,崔冉冉. 关于环的Q-clean性及Q-clean corner的讨论[J]. 《山东大学学报(理学版)》, 2020, 55(2): 79-83.

SUN Xiao-qing, XIAO Yan-ting, CUI ran-ran. Discussions on the Q-cleanness of rings and Q-clean corner[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 79-83.

参考文献

[1] NICHOLSON W K. Lifting idempotents and exchange rings[J]. Journal of the American Mathematical Society, 1977, 229:269-278.
[2] ARA P, PEDERSEN G K, PEREVA F. An infinite analogue of rings with stable range one[J]. Journal of Algebra, 2000, 230:608-655.
[3] BROWN L G, PERDERSEN G K. On the geometry of the unit ball of a C^*-algebra[J]. Journal für die Reine und Angewandte Mathematik, 1995, 469:113-147.
[4] CASTRO-GONZÁLEZ N, CHEN Jianlong, WANG L. Further results on generalized inverses in rings with involution[J]. Electronic Journal of Linear Algebra, 2015, 30:118-134.
[5] HAN J, NICHOLSON W K. Extensions of clean rings[J]. Communications in Algebra, 2001, 29:2589-2596.

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关于环的Q-clean性及Q-clean corner的讨论

Discussions on the Q-cleanness of rings and Q-clean corner

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