On Quasipolar Rings
On Quasipolar Rings
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DOI：
10.1142/s1005386712000557
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发表时间：
2012-10
影响因子：
0.3
通讯作者：
Zhiling Ying;Jianlong Chen
中科院分区：
文献类型：
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作者：
Zhiling Ying;Jianlong Chen
环的准极元的概念由 Koliha 和 Patricio 于 2002 年提出。在本文中，我们介绍了准极环的概念，并将其与环理论中其他熟悉的概念联系起来。证明了强π正则环和唯一洁净环都是准极性环，并且准极性环也是强洁净环，但没有两类环是等价的。对于交换环，准极环与半规则环重合。还证明了任意交换唯一洁净环或交换局部环上的每一个n×n上三角矩阵环都是准极性的。
The notion of quasipolar elements of rings was introduced by Koliha and Patricio in 2002. In this paper, we introduce the notion of quasipolar rings and relate it to other familiar notions in ring theory. It is proved that both strongly π-regular rings and uniquely clean rings are quasipolar, and quasipolar rings are strongly clean, but no two of these classes of rings are equivalent. For commutative rings, quasipolar rings coincide with semiregular rings. It is also proved that every n × n upper triangular matrix ring over any commutative uniquely clean ring or commutative local ring is quasipolar.