| 单位正则环中的零化子 |
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| 引用本文： | 陈焕艮.单位正则环中的零化子[J].杭州师范学院学报(自然科学版),2010,9(1). |
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| 作者姓名： | 陈焕艮 |
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| 作者单位： | 杭州师范大学,理学院,浙江,杭州,310036 |
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| 摘 要： | 环R称为单位正则环,如果对任何x∈R,有可逆元u∈R使得x=xux.文章利用零化子刻画了单位正则环,证明了正则环是单位正则环当仅当l(a)∩l(b)=l(d)时,有y∈R使得l(a)∩l(b)=t(a+by),当仅当l(a)=l(b)时,有u∈U(R)使得a=bua.
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| 关 键 词： | 零化子 单位正则环 稳定秩1 |
Annihilators in Unit-Regular Rings |
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| Abstract: | A ring R is unit-regular provided that for any x∈R,there exists an invertible u∈R such that x=xux.The paper has characterized the unit-regular ring by means of annihilators,proved that a regular ring R is unit-regular if and only if whenever l(a)∩l(b)=l(d),there exists y∈R such that l(a)∩l(b)=l(a+by),and if and only if whenever l(a)=l(b),there exists u∈U(R) such that a=bua. |
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| Keywords: | annihilator unit-regular ring stable range one |
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