| 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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| 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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