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研究生:張介玉
研究生(外文):Chie-Yu Chang
論文名稱:環上的導算及廣義導算
論文名稱(外文):Some results on derivations and generalized derivations in rings
指導教授:林哲雄林哲雄引用關係
指導教授(外文):Jer-Shyong Lin
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:21
中文關鍵詞:導算廣義導算
外文關鍵詞:ringsderivationsgeneralized derivations
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1.質環上具有導算的子環
假定R是一個非交換且特徵數不為2的質環, 且d是R上的非零導算.並假定U是不在中心的Lie理想且U^{d}亦不在中心. 若d是一個外導算, 則由{[d(x),x];x屬於U}生成的子環包含一個非零的理想但必須排除R滿足S_4.
2.半質環上的喬登廣義導算
假定R是一個特徵數不為2的半質環, 則R上的每個喬登廣義導算都是廣義導算.

1. On certain subrings of prime rings with derivations
Let R be a noncommutative prime ring with nonzero derivation d. U is a noncentral Lie ideal of R and U^{d} is not contained in Z. If d is outer, then the subring of R generated by {[d(x),x] ;x belong to U} contains a nonzero ideal of R except charR=2 and R satisfies S_{4}.
2. Jordan generalized derivations on semiprime rings
Let R be a 2-torson free semiprime ring, then every Jordan generalized derivation on R is a generalized derivation.

Introduction
Preliminaries
ChapterⅠ. On certain subrings of prime rings with derivations
ChapterⅡ. Jordan generalized derivations on semiprime rings
References

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[12] C.-L Chung. The additive subgroup generalized by a polymial. Isr. J. Math. vol 59, (1987), 98-106.
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[15] B. Havla, Generalized derivations in rings. Comm Algebra 26, (1998), 1147-1166.
[16] V. K. Kharchenko, Differential identities of semiprime rings. Algebra and Logic 18 (1979 ), 58-80.
[17] T.-K Lee, Semiprime rings with differential identities. Bull. Inst. Math. Acad. Sinca. 20 (1992), 27-38.
[18] P.-H Lee and T.-K Lee, On derivations of prime rings. Chinese J.Math 9 (1981), 107-110.
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[22] T.-L Wong, On certain subgroups of semiprime rings with derivations. to appear.

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