Generalized skew derivations on triangular algebras determined by action on zero products

For a triangular algebra and an automorphism σ of , we describe linear maps F,G: → satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈ are such that xy = 0. In particular, when is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of th...

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Bibliographic Details
Published inCommunications in algebra Vol. 46; no. 5; pp. 1859 - 1867
Main Authors Benkovic, Dominik, Grasic, Mateja
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2018
Taylor & Francis Ltd
Subjects
Algebra
Automorphisms
Derivation
generalized derivable mapping at zero point
generalized skew derivation
triangular algebra
zero product determined algebra
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Summary:For a triangular algebra and an automorphism σ of , we describe linear maps F,G: → satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈ are such that xy = 0. In particular, when 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∈ , where D: → is a skew derivation. When is not zero product determined, we show that there are also nonstandard solutions for maps F and G.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2017.1360334