• Title, Summary, Keyword: bi-derivation

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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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ON SYMMETRIC BI-GENERALIZED DERIVATIONS OF LATTICE IMPLICATION ALGEBRAS

  • Kim, Kyung Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.32 no.2
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    • pp.179-189
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    • 2019
  • In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

ON THE STABILITY OF BI-DERIVATIONS IN BANACH ALGEBRAS

  • Jung, Yong-Soo;Park, Kyoo-Hong
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.5
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    • pp.959-967
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    • 2011
  • Let A be a Banach algebra and let f : $A{\times}A{\rightarrow}A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f : $A{\times}A{\rightarrow}A$ is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f = 0.

SYMMETRIC BI-(f, g)-DERIVATIONS IN LATTICES

  • Kim, Kyung Ho;Lee, Yong Hoon
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.3
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    • pp.491-502
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    • 2016
  • In this paper, as a generalization of symmetric bi-derivations and symmetric bi-f-derivations of a lattice, we introduce the notion of symmetric bi-(f, g)-derivations of a lattice. Also, we define the isotone symmetric bi-(f, g)-derivation and obtain some interesting results about isotone. Using the notion of $Fix_a(L)$ and KerD, we give some characterization of symmetric bi-(f, g)-derivations in a lattice.