| J-半单亚直既约环类确定的上限 |
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| 引用本文： | 杨宗文,王俊民.J-半单亚直既约环类确定的上限[J].数学研究及应用,2000,20(4):503-506. |
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| 作者姓名： | 杨宗文 王俊民 |
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| 作者单位： | 云南大学数学系;云南大学数学系 |
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| 摘 要： | Ｆ．Ａ．Ｓｚａｓｚ在［１］中提出公开问题５５：设Ｋ是Ｊａｃｏｂｓｏｎ根为零的全体亚直既约环类，研究类Ｋ确定的上根．本文对此进行了研究，证明了Ｊａｃｏｂｓｏｎ根为零的全体亚直既约环类Ｋ确定的上根Ｒ是特殊根，它介于Ｊａｃｏｂｓｏｎ根与Ｂｒｏｗｎ－ＭｃＣｏｙ根之间．并给出任意结合环Ａ为Ｒ－根环的充要条件．
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| 关 键 词： | J－半单亚直既约环类 Jacobson根 结合环 R－根环 Brown－McCoy根 |
| 收稿时间： | 2/3/1997 12:00:00 AM |
The Upper Radical Determined by the Class of all J-Semisimple Subdirectly Irreducible Rings |
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| YANG Zong-wen and WANG Jun-min.The Upper Radical Determined by the Class of all J-Semisimple Subdirectly Irreducible Rings[J].Journal of Mathematical Research with Applications,2000,20(4):503-506. |
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| Authors: | YANG Zong-wen and WANG Jun-min |
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| Institution: | Dept. of Math.; Yunnan University; Kunming; China;Dept. of Math.; Yunnan University; Kunming; China |
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| Abstract: | F.A.Szasz has put forward the open problem 55 in 1]: Let K be the class of all subdirectly irreducible rings, whose Jacobson radical is (0). Examine the upper radical determined by the class K. In this paper, the problem has been examined. (1) It has been proved that the upper radical R determined by the class K is a special radical,which lies between Jacobson radical and Brown-McCoy radical. (2) It has been given some necessary and sufficient condition of ring A to be an R-radical ring. |
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| Keywords: | subdirectly irreducible ring special radical antisimple radical MHR-ring Jacobson radical |
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