陈维新.左零因子理想具升键条件之Г-环和广义Г-环[J].数学研究及应用,1985,5(2):1~4
左零因子理想具升键条件之Г-环和广义Г-环
The Г-rings and Generalized Г-rings with Ascending Chain Condition on Left Zero Divisor Ideals
投稿时间:1982-06-01  
DOI:10.3770/j.issn:1000-341X.1985.02.001
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陈维新 浙江大学 
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      In this paper the following result is obtained:(*): If Г-ring A satisfies ascending chain condition on left zero divisor ideals, then every strongly nil right ideal is strongly nilpotent.In order that (*) may contain the corresponding result of associative rings, a new concept, generalized Г-ring is introduced. So that any associative ring is naturally explained as a generalized Г-ring. It is proved that (*) is valid in the generalized Г-rings, thence the result of associative rings is a special case in the generalized Г-rings.
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