完全分配交换子空间格代数上的乘性广义李n导

Pub Date : 2023-01-01 DOI:10.7153/oam-2023-17-10

Fei Ma, Min Yin

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引用次数: 0

摘要

．设Alg L是一个完全分配交换子空间格代数，设δ: Alg L→Alg L是一个非线性映射。结果表明,δ是乘法广义n推导躺在Alg L有一个关联的乘法广义谎言n推导d当且仅当δ(a) =ψ(a) +ξ(a)适用于每一个∈Alg L,ψ:Alg L→Alg L是一个添加剂广义推导和ξ:Alg L→Z (Alg L)是一个central-valued地图消失在每个(n−1)th换向器p n(1, 2,···,n)。

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Multiplicative generalized Lie n-derivations on completely distributive commutative subspace lattice algebras

. Let Alg L be a completely distributive commutative subspace lattice algebra and let δ : Alg L → Alg L be a nonlinear map. It is shown that δ is a multiplicative generalized Lie n -derivation on Alg L with an associated multiplicative generalized Lie n -derivation d if and only if δ ( A ) = ψ ( A )+ ξ ( A ) holds for every A ∈ Alg L , where ψ : Alg L → Alg L is an additive generalized derivation and ξ : Alg L → Z ( Alg L ) is a central-valued map vanishing on each ( n − 1 ) -th commutator p n ( A 1 , A 2 , ··· , A n ) .

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