| 半素环与 Morphic 环 |
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| 引用本文： | 刘钢,储茂权.半素环与 Morphic 环[J].安庆师范学院学报(自然科学版),2009,15(1):4-5. |
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| 作者姓名： | 刘钢 储茂权 |
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| 作者单位： | 安徽师范大学,数学计算机科学学院,安徽,芜湖,241000;宿州学院,数学系,安徽,宿州,234000;宿州学院,数学系,安徽,宿州,234000 |
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| 基金项目： | 安徽省教育厅自然科学基金 |
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| 摘 要： | 本文中，我们证明了如下主要结果：（1）如果R是半素环，R又是右Morphic的，且L是R中的极大左零化子，则L是R的极大左理想，且存在e^2=e∈R使L=Re。（2）如果R是素环又是右Morphie的，且有极大左零化子，则R是左、右本原环（3）如果R是半素的右Morphic环，则R有唯一的最大理想I，I不含非零幂零元且I=lr（I）=rl（I），Z（RI）=Z（IR）=0。
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| 关 键 词： | 半素环 素环 右Morphic环 左、右本原环 |
Semi-Prime Ring and Morphic Ring |
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| LIU Gang,CHU Mao-quan.Semi-Prime Ring and Morphic Ring[J].Journal of Anqing Teachers College(Natural Science Edition),2009,15(1):4-5. |
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| Authors: | LIU Gang CHU Mao-quan |
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| Institution: | LIU Gang , CHU Mao-quan (1. School of Mathematics and Computer Science, Anhui Normal University,Wuhu 241000; 2. Department of Mathematics, Suzhou College,Suzhou 234000,China) |
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| Abstract: | In this paper,we prove the following results :(1) If R is a semi-prime ring,right-morphic and L is a maximal left annihilator in R,then L is a maximal left idea of R and there exist e2=e∈R such that L=Re.(2) If R is a semi-prime right-morphic ring and has a maximal left annihilator,then R is a left and right primitive ring.(3)If R is a semiprime right-morphic ring,then there is the unique largest two-sided idea I that contains no nonzero nilpotent elements,moreover I=lr(I)=rl(I),Z(RI)=Z(IR)=0. |
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| Keywords: | semi-prime ring prime ring right-morphic ring left-right primitive ring |
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