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容纳一个非零导子的分配生成素近环 被引量:3

DISTRIBUTIVELY-GENERATED PRIME NEAR-RINGS ADMITTING A NONZERO DERIVATION
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摘要 设N是一个2—挠自由分配生成素近环,它具有单位元1和中心Z。本文证明了;如果N满足下列条件之一,则N是交换整区:(1)N容纳一个非零导子D使得容纳一个非零导子D使得x,y∈N,[D(x),D2(y)]=0,并且D(N)不含非零的幂零元. Let N be a 2-torsion-free distributively generated prime near-ring with identity 1 and the center Z. It is shown that N is a commutative domain if it satisfies one of the following conditions: (l ) N admits a nonzero derivation D such that D2(N) Z ; (2)N admits anonzero derivation D such that[ D(x), D2 (y) ]= 0,x,y ∈ N, and D(N) haven't nonzero nilpotent elements.
作者 王学宽
出处 《湖北大学学报(自然科学版)》 CAS 1994年第2期135-138,共4页 Journal of Hubei University:Natural Science
关键词 导子 分配生成 素近环 交换子 环论 Derivation Distributively generated prime near-ring Torsion-free Commutator Localization
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同被引文献9

  • 1[1]Bell H E,Mason G.On derivations in prime near-rings.Bestch G.Near-rings and nearfields[M].New York:North-Holland,1987.31~35.
  • 2[3]Lee P H,Lee T K.On derivations of prime rings[J].Chinese Journal of Mathematic,1981,9(2):107~110.
  • 3[4]Frohlich A.Distributively-generated near-rings[J].Ideal Theory Proc London Math Soc,1958,8(3):76~94.
  • 4[5]Posner E C.Derivations in prime rings[J].Proc Amer Math Soc,1957,8:1 093~1 100.
  • 5[6]Herstein I N.Rings with involution[M].Chicago:Chicago Univ Press,1976.
  • 6[7]Herstein I N.A note on derivations II[J].Canal Math Bull,1979,22:509~511.
  • 7[8]Wang Xuekuan.Derivations in prime near-rings[J].Proc Amer Math Soc,1994,121:361~366.
  • 8王学宽,湖北大学学报,1994年,16卷,135页
  • 9王学宽,Proc Amer Math Soc,1994年,121卷,361页

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