A QUESTION ON *-REGULAR RINGS
- Resource Type
- Article
- Authors
- Jian Cui; Xiaobin Yin
- Source
- 대한수학회보, 55(5), pp.1333-1338 Sep, 2018
- Subject
- 수학
- Language
- English
- ISSN
- 2234-3016
1015-8634
A $*$-ring $R$ is called $*$-regular if every principal one-sided ideal of $R$ is generated by a projection. In this note, several characterizations of $*$-regular rings are provided. In particular, it is shown that a matrix ring $M_n(R)$ is $*$-regular if and only if $R$ is regular and $1+x_1^*x_1+\cdots+x_{n-1}^*x_{n-1}$ is a unit for all $x_i$ of $R;$ which answers a question raised in the literature recently.