• Title, Summary, Keyword: 3-derivation

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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.

Generalized Derivations on ∗-prime Rings

  • Ashraf, Mohammad;Jamal, Malik Rashid
    • Kyungpook Mathematical Journal
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    • v.58 no.3
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    • pp.481-488
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    • 2018
  • Let I be a ${\ast}$-ideal on a 2-torsion free ${\ast}$-prime ring and $F:R{\rightarrow}R$ a generalized derivation with an associated derivation $d:R{\rightarrow}R$. The aim of this paper is to explore the condition under which generalized derivation F becomes a left centralizer i.e., associated derivation d becomes a trivial map (i.e., zero map) on R.

ON PRIME AND SEMIPRIME RINGS WITH PERMUTING 3-DERIVATIONS

  • Jung, Yong-Soo;Park, Kyoo-Hong
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.789-794
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    • 2007
  • Let R be a 3-torsion free semiprime ring and let I be a nonzero two-sided ideal of R. Suppose that there exists a permuting 3-derivation ${\Delta}:R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on I. Then the trace of ${\Delta}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

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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A NOTE ON DERIVATIONS OF ORDERED ��-SEMIRINGS

  • Kim, Kyung Ho
    • Korean Journal of Mathematics
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    • v.27 no.3
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    • pp.779-791
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    • 2019
  • In this paper, we consider derivation of an ordered ${\Gamma}$-semiring and introduce the notion of reverse derivation on ordered ${\Gamma}$-semiring. Also, we obtain some interesting related properties. Let I be a nonzero ideal of prime ordered ${\Gamma}$-semiring M and let d be a nonzero derivation of M. If ${\Gamma}$-semiring M is negatively ordered, then d is nonzero on I.

DERIVATIONS OF UP-ALGEBRAS

  • Sawika, Kaewta;Intasan, Rossukon;Kaewwasri, Arocha;Iampan, Aiyared
    • Korean Journal of Mathematics
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    • v.24 no.3
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    • pp.345-367
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    • 2016
  • The concept of derivations of BCI-algebras was first introduced by Jun and Xin. In this paper, we introduce the notions of (l, r)-derivations, (r, l)-derivations and derivations of UP-algebras and investigate some related properties. In addition, we define two subsets $Ker_d(A)$ and $Fix_d(A)$ for some derivation d of a UP-algebra A, and we consider some properties of these as well.