Generalized skew derivations on triangular algebras determined by action on zero products |
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Authors: | Dominik Benkovič |
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Affiliation: | Department of Mathematics and Computer Science, FNM, University of Maribor, Maribor, Slovenia |
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Abstract: | For a triangular algebra 𝒜 and an automorphism σ of 𝒜, we describe linear maps F,G:𝒜→𝒜 satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈𝒜 are such that xy = 0. In particular, when 𝒜 is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈𝒜, where D:𝒜→𝒜 is a skew derivation. When 𝒜 is not zero product determined, we show that there are also nonstandard solutions for maps F and G. |
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Keywords: | Derivation generalized derivable mapping at zero point generalized skew derivation triangular algebra zero product determined algebra |
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