• 제목/요약/키워드: Generalized Derivation

검색결과 162건 처리시간 0.018초

ON GENERALIZED JORDAN DERIVATIONS OF GENERALIZED MATRIX ALGEBRAS

  • Ashraf, Mohammad;Jabeen, Aisha
    • 대한수학회논문집
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    • 제35권3호
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    • pp.733-744
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    • 2020
  • Let 𝕽 be a commutative ring with unity, A and B be 𝕽-algebras, M be a (A, B)-bimodule and N be a (B, A)-bimodule. The 𝕽-algebra 𝕾 = 𝕾(A, M, N, B) is a generalized matrix algebra defined by the Morita context (A, B, M, N, 𝝃MN, ΩNM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.

Generalized Derivations on ∗-prime Rings

  • Ashraf, Mohammad;Jamal, Malik Rashid
    • Kyungpook Mathematical Journal
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    • 제58권3호
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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.

COMMUTATIVITY OF MULTIPLICATIVE b-GENERALIZED DERIVATIONS OF PRIME RINGS

  • Muzibur Rahman Mozumder;Wasim Ahmed;Mohd Arif Raza;Adnan Abbasi
    • Korean Journal of Mathematics
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    • 제31권1호
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    • pp.95-107
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    • 2023
  • Consider ℛ to be an associative prime ring and 𝒦 to be a nonzero dense ideal of ℛ. A mapping (need not be additive) ℱ : ℛ → 𝒬mr associated with derivation d : ℛ → ℛ is called a multiplicative b-generalized derivation if ℱ(αδ) = ℱ(α)δ +bαd(δ) holds for all α, δ ∈ ℛ and for any fixed (0 ≠)b ∈ 𝒬s ⊆ 𝒬mr. In this manuscript, we study the commutativity of prime rings when the map b-generalized derivation satisfies the strong commutativity preserving condition and moreover, we investigate the commutativity of prime rings that admit multiplicative b-generalized derivation, which improves many results in the literature.

ON SYMMETRIC BI-GENERALIZED DERIVATIONS OF LATTICE IMPLICATION ALGEBRAS

  • Kim, Kyung Ho
    • 충청수학회지
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    • 제32권2호
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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 $x,y,z{\in}L$.

JORDAN GENERALIZED DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS

  • Bahmani, Mohammad Ali;Bennis, Driss;Vishki, Hamid Reza Ebrahimi;Attar, Azam Erfanian;Fahid, Barahim
    • 대한수학회논문집
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    • 제33권3호
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    • pp.721-739
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    • 2018
  • In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a "generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).