RINGS WITH ANNIHILATOR CHAIN-CONDITIONS AND RIGHT DISTRIBUTIVE RINGS

被引：7
|
作者：
FERRERO, M [1 ]
TORNER, G [1 ]
机构：
[1] UNIV DUISBURG,FACHBEREICH MATH,W-4100 DUISBURG,GERMANY
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1993年 / 119卷 / 02期
关键词：
D O I：
10.2307/2159920
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that if a right distributive ring R, which has at least one completely prime ideal contained in the Jacobson radical, satisfies either a.c.c or d.c.c. on principal right annihilators, then the prime radical of R is the right singular ideal of R and is completely prime and nilpotent. These results generalize a theorem by Posner for right chain rings.
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页码：401 / 405
页数：5
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