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研究生:姚宏宗
研究生(外文):Hung-Tzung Yao
論文名稱:對合環上的導算
論文名稱(外文):Derivations in Prime Rings with Involution
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:33
中文關鍵詞:質環對合環導算
外文關鍵詞:pring ringsring with involutionderivation
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給定一個特徵數不為2的對合環R, 並給定d_1, d_2是R上非零的導算且對所有R的元素x都滿足d_i(x^{*})=-(d_i(x))^{*}. 假設C的個數大於等於5且對於所有R上對稱的元素s都滿足d_1(s)d_2(s)=0, 則R滿足S_4.

Let R be a prime ring of characteristic not 2 with involution * and for each i=1,2, d_i be a nonzero derivation on R such that d_i(x^{*})=-(d_i(x))^{*} for all x in R. Suppose that |C|≧5 and d_1(s)d_2(s)=0 for all s in S, then R is either a commutative domain or an order in a 4-dimensional central simple algebra.

1INTRODUCTION
2PRELIMINARIES
2.1Martindale's Quotient Rings
2.2Involutions
2.3Derivations
3MAIN THEOREM
Reference

K. I. Beidar, W. S. Martindale and A. V. Mikhalev, "Rings with Generalized Identities," New York/Basel/Hong Kong, 1996.
Matej Bresar, M. A. Chebotar and Peter Semrl, On derivations of prime rings *, Communications In Algebra 27(7),(1999), 3129-3135.
C. L. Chuang, *-differential identites of prime rings with involution, Trans. Amer. Math. Soc. 316(1989), 251-279.
T. S. Erickson, W. S. Martindale and J. M. Osborn, Prime nonassociative algebras, Pacific J. Math. 60(1975),49-63.
I. N. Herstein, "Rings with Involution," Univ. Chicago Press, Chicago, 1976.
I. N. Herstein, A theorem on derivations of prime rings with involution, Canadian J. Math. 34(1982), 356-369.
I. N. Herstein, Center-like elements in prime rings, J. Algebra 60(1979), 567-574.
I. N. Herstein, Derivations of prime rings having power central values, Contemporary Math. 13(1982),163-171.
V. K. Kharchenko, Differential identities of prime rings, Algebra i Logoka 17(1978), 220-238.
P. H. Lee and H. H. Shih, Skew *-derivations with power-central values, Communications In Algebra 24(10),(1996), 3247-3257.
P. H. Lee and T. L. Wong, Derivations cocentralizing lie ideals, Bull. Inst. Math. Acad. Sinica, 23(1995), 1-5.
J. S. Lin, On derivations of prime rings with involution, Chinese J.Math. 14(1986), 37-51.

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