| 环的QG—根 |
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| 引用本文： | 陈培慈.环的QG—根[J].江西师范大学学报(自然科学版),1989,13(1):5-11,27. |
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| 作者姓名： | 陈培慈 |
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| 作者单位： | 江西师范大学数学系 |
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| 摘 要： | 本文定义环R的QG—根为R的所有Small理想之和,它适应于非结合环。定理2和5给出了QG(R)和QG—半单环的刻划,定理3和4给出了QG(R)和Jacobson与Brown—McCoy根及的一般根论的联系,定理1和8给出了一个环分解成单环直和的苦干充要条件,最后,定义投射环和拟半完备环的概念,从而给出一个关于QG(R)是R的Small理想的充分条件。
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| 关 键 词： | Small理想 OG根 投射环 拟半完备环 |
QG-Radicals of Rings |
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| Chen Peici.QG-Radicals of Rings[J].Journal of Jiangxi Normal University (Natural Sciences Edition),1989,13(1):5-11,27. |
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| Authors: | Chen Peici |
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| Institution: | Dept. of Math. |
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| Abstract: | In this paper we have defined the QG-radical QG (R) of a ring R is the sum of all Small ideals of R. It applies to non-associative rings. The structures of QG ( R ) and QG-semisimple rings were given in the theorems 2 and5. We have given the relations between the QG-radical and Jacobson and Brown-McCoy radicals in the theorems 3 and 4. Finally, we have defined the protective ring and the Quasi-semiperfect ring, and have given a sufficient condition that the QG(R)will be a small ideal of R. |
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