| 零因子环与相关环 |
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| 引用本文： | 任艳丽,王尧.零因子环与相关环[J].吉首大学学报(自然科学版),2013,34(1):1-5. |
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| 作者姓名： | 任艳丽 王尧 |
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| 作者单位： | （1.南京晓庄学院数学与信息技术学院，江苏 南京 211171;2.南京信息工程大学数学与统计学院，江苏 南京 210044） |
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| 基金项目： | National Natural Science Foundation of China(11071097;11101217);Natural Science Foundation of the Education Department of Jiangsu Province(11KJB110007) |
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| 摘 要： | 提出左（右）零因子环的概念，它们是一类没有单位元的环.一个环称为左（右）零因子环，如果对于任何a∈R,都有rR(a)≠0（lR(a)≠0）.讨论了左（右）零因子环和相关环的关系，给出左零因子环的一些特征刻画.
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| 关 键 词： | 零因子 左零因子环 可逆环 对称环 半交换环 p.p.-环 Armendariz 环 |
Zero-Divisor Rings and Related Rings |
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| REN Yan-li
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WANG Yao.Zero-Divisor Rings and Related Rings[J].Journal of Jishou University(Natural Science Edition),2013,34(1):1-5. |
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| Authors: | REN Yan-li WANG Yao |
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| Institution: | (1.School of Mathematics and Information Technology,Nanjing Xiaozhuang University,Nanjing 211171,China;2.School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China) |
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| Abstract: | The authors introduce the concepts of left (right) zero-divisor rings,a class of rings without identity.A ring R is called left (right) zero-divisor if rR(a)≠0(lR(a)≠0) for every a∈R.The authors investigate the relations between left (right) zero-divisor rings and related rings,and give equivalent characterizations of left zero-divisor rings. |
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| Keywords: | zero-divisor left zero-divisor ring reversible ring symmetric ring semicommutative ring p p -ring Armendariz ring |
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