陈维新.Γ-环和广义Γ-环的强幂零性[J].数学研究及应用,1984,4(4):3~9
Γ-环和广义Γ-环的强幂零性
On the Strongly Nilpotency of Г-rings and Generalized Г-rings
投稿时间:1981-11-06  
DOI:10.3770/j.issn:1000-341X.1984.04.002
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陈维新 浙江大学 
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      In this paper, we study the strongly nilpotency of Γ-rings and generalized Γ-rings.(Ⅰ) With what conditions is a strongly nil subring of Γ-rings strongly nilpotent?(Ⅱ) With what conditions is a nil subring of Γ-rings strongly nilpotent?For(Ⅰ), the condition is one of the following conditions:(1) ascending chain condition on the- strongly nilpotent subrings.(2) Noether's condition.(3) Goldie's condition.(4) ascending chain condition on right annihilators and on left annihilators. For(Ⅱ), the conditions is (2) or (3). In order that the above results may contain the corresponding results of associative rings, a new concept, generalized Γ-ring is introduced, so that any associative ring is naturally explained as a generalized Γ-ring. It is proved that the above results are valid in generalized Γ-rings. Thence the well-known results of associative rings are special cases in generalized Γ-rings.
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