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Rings in which Every Element Is A Left Zero-Divisor

期刊名称：Journal of Mathematical Research with Applications
时间：2013
页码：403-411
分类：O121.5[理学—数学;理学—基础数学] TS934.3[轻工技术与工程]
作者机构：[1]School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Jiangsu 211171, P. R. China, [2]School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Jiangsu 210044, P. R. China
相关基金：Supported by the National Natural Science Foundation of China （Grant Nos. 11071097; 11101217）.
相关项目：Poisson代数的结构与K_0群

作者：王尧, 任艳丽|

关键词：除数, 戒指, 元素, 电话咨询, 有限子集, 等价刻画, RFA, 零环, zero-divisor, left zero-divisor ring, strong left zero-divisor ring, RFA ring, extensions of rings.

中文摘要：

We introduce the concepts of left (right) zero-divisor rings, a class of rings without identity. We call a ring R left (right) zero-divisor if rR (a) = 0 (lR (a) = 0) for every a∈R, and call R strong left (right) zero-divisor if rR(R) = 0 (lR(R) = 0). Camillo and Nielson called a ring right finite annihilated (RFA) if every finite subset has non-zero right annihilator. We present in this paper some basic examples of left zero-divisor rings, and investigate the extensions of strong left zero-divisor rings and RFA rings, giving their equivalent characterizations.

英文摘要：

We introduce the concepts of left （right） zero-divisor rings, a class of rings without identity. We call a ring R left （right） zero-divisor if rR（a） ≠ 0（lR（a） ≠ 0） for every a∈ R, and call R strong left （right） zero-divisor if r R （R）≠0（lR（R）≠ 0）. Camillo and Nielson called a ring right finite annihilated （RFA） if every finite subset has non-zero right annihilator. We present in this paper some basic examples of left zero-divisor rings, and investigate the extensions of strong left zero-divisor rings and RFA rings, giving their equivalent characterizations.

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