| 中间超素环和中间超素根 |
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| 引用本文： | 张宪君,于淑兰.中间超素环和中间超素根[J].黑龙江大学自然科学学报,2007,24(1):16-18. |
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| 作者姓名： | 张宪君 于淑兰 |
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| 作者单位： | 1. 哈尔滨工业大学(威海),数学系,山东,威海,264209
2. 山东大学威海分校,数学系,山东,威海,264209 |
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| 摘 要： | 一个环R中的非零元a被称为一个中间零因子,如果存在R的非零元x和y,使得xay=0.一个环R称为中间超素环,如果它的每个非零理想都包含一个非零元素,它不是中间零因子.给出了一个环是中间超素环的一些等价条件,并证明了由所有的中间超素环组成的环类所确定的上根,即中间超素根,是一个特殊根.最后给出了中间超素根与常见的一些特殊根之间的关系.
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| 关 键 词： | 中间超素环 中间超素根 特殊根 |
| 文章编号： | 1001-7011(2007)01-0016-03 |
| 修稿时间： | 2006年3月31日 |
The middle superprime rings and middle superprime radical |
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| ZHANG Xian-jun,YU Shu-lan.The middle superprime rings and middle superprime radical[J].Journal of Natural Science of Heilongjiang University,2007,24(1):16-18. |
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| Authors: | ZHANG Xian-jun YU Shu-lan |
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| Abstract: | An element a in ring R is called middle divisor of zero,if there exist non-zero elements x and y in R such that xay=0. An ring R is said to be the middle superprime ring,if every non-zero ideal of R contains an non-zero element c, which is not middle divisor of zero. Some equivalent conditions that a ring is middle superprime ring are given, and it is shown that the upper radical determined by the class of the all middle superprime rings is a special radical. Lastly, the relationship between the middle superprime radical and usual special radicals is given. |
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| Keywords: | middle superprime ring middle superprime radical special radical |
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