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- W2021901738 abstract "Let R be a ring and U be a Lie ideal of R. Suppose that σ, τ are endomorphisms of R. A family D = {d n }n ∈ Nof additive mappings d n :R → R is said to be a (σ,τ)- higher derivation of U into R if d0 = I R , the identity map on R and holds for all a, b ∈ U and for each n ∈ N. A family F = {f n }n ∈ Nof additive mappings f n :R → R is said to be a generalized (σ,τ)- higher derivation (resp. generalized Jordan (σ,τ)-higher derivation) of U into R if there exists a (σ,τ)- higher derivation D = {d n }n ∈ Nof U into R such that, f0 = I R and (resp. holds for all a, b ∈ U and for each n ∈ N. It can be easily observed that every generalized (σ,τ)-higher derivation of U into R is a generalized Jordan (σ,τ)-higher derivation of U into R but not conversely. In the present paper we shall obtain the conditions under which every generalized Jordan (σ,τ)- higher derivation of U into R is a generalized (σ,τ)-higher derivation of U into R." @default.
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- W2021901738 date "2012-10-06" @default.
- W2021901738 modified "2023-10-18" @default.
- W2021901738 title "Generalized (σ,τ) higher derivations in prime rings" @default.
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- W2021901738 doi "https://doi.org/10.1186/2193-1801-1-31" @default.
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