| Rings in which Every Element Is A Left Zero-Divisor |
| Received:May 10, 2012 Revised:November 22, 2012 |
| Key Words:
zero-divisor left zero-divisor ring strong left zero-divisor ring RFA ring extensions of rings.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11071097; 11101217). |
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| Abstract: |
| 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 $r_{R}(a) \neq 0~(l_{R}(a) \neq 0)$ for every $a\in R$, and call $R$ strong left (right) zero-divisor if $r _{R} (R) \neq 0$~($l_{R}(R) \neq 0$). 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.04.003 |
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