• Title, Summary, Keyword: derivation

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THE STABILITY OF A DERIVATION ON A BANACH ALGEBRA

  • LEE, EUN HWI;CHANG, ICK-SOON;JUNG, YONG-SOO
    • Honam Mathematical Journal
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    • v.28 no.1
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    • pp.113-124
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    • 2006
  • In this article, we show that for an approximate derivation on a Banach *-algebra, there exist a unique derivation near the an approximate derivation and for an approximate derivation on a $C^*$-algebra, there exist a unique derivation near the approximate derivation.

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LOCAL DERIVATIONS OF THE POLYNOMIAL RING OVER A FIELD

  • Yon, Yong-Ho
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.247-257
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    • 1999
  • In this article, we give an example of local derivation, that is not derivation, on the algebra F(x1,…, xn) of rational functions in x1, …, xn over an infinite field F, and show that if X is a set of symbols and {x1,…, xn} is a finite subset of X, n$\geq$1, then each local derivation of F[x1,…, xn] into F[X] is a F-derivation and each local derivation of F[X] into itself is also a F-derivation.

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LEFT DERIVATIONS ON BANACH ALGEBRAS

  • Jung, Yong-Soo
    • Journal of the Chungcheong Mathematical Society
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    • v.8 no.1
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    • pp.37-44
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    • 1995
  • In this paper we show that every left derivation on a semiprime Banach algebra A is a derivation which maps A into the intersection of the center of A and the Jacobson radical of A, and hence every left derivation on a semisimple Banach algebra is zero.

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ON LEFT DERIVATIONS AND DERIVATIONS OF BANACH ALGEBRAS

  • Jung, Yong-Soo
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.659-667
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    • 1998
  • In this paper we show that every left derivation on a semiprime Banach algebra A is a derivation which maps A into the intersection of the center of A and the Jacobson radical of A, and hence every left derivation on a semisimple Banach algebra is always zero.

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DERIVATIONS ON SUBRINGS OF MATRIX RINGS

  • Chun, Jang-Ho;Park, June-Won
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.3
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    • pp.635-644
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    • 2006
  • For a lower niltriangular matrix ring $A=NT_n(K)(n{\geq}3)$, we show that every derivation of A is a sum of certain diagonal, trivial extension and strongly nilpotent derivation. Moreover, a strongly nilpotent derivation is a sum of an inner derivation and an uaz-derivation.

ON GENERALIZED SYMMETRIC BI-DERIVATIONS IN PRIME RINGS

  • Ozturk, M. Ali;Sapanci, Mehmet
    • East Asian mathematical journal
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    • v.15 no.2
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    • pp.165-176
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    • 1999
  • After the derivation was defined in [19] by Posner a lot of researchers studied the derivations in ring theory in different manners such as in [2], [4], [5], ..., etc. Furthermore, many researches followed the definition of the generalized derivation([3], [6], [7], ..., etc.). Finally, Maksa defined a symmetric bi-derivation and many researches have been done in ring theory by using this definition. In this work, defining a symmetric bi-$\alpha$-derivation, we study the mentioned researches above in the light of this new concept.

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