VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Generalized derivations on unital algebras determined by action on zero products
    Benkovič, Dominik ; Grašič, Mateja, 1983-
    Let ▫$\mathcal{A}$▫ be a unital algebra having a nontrivial idempotent and let ▫$\mathcal{M}$▫ be a unitary ▫$\mathcal{A}$▫-bimodule. We consider linear maps ▫$F,G \colon \mathcal{A} \to ... \mathcal{M}$▫ satisfying ▫$F(x)y + xG(y) = 0$▫ whenever ▫$x, \, y \in \mathcal{A}$▫ are such that ▫$xy = 0$▫. For example, when ▫$\mathcal{A}$▫ is zero product determined algebra (e.g. algebra generated by idempotents) ▫$F$▫ and ▫$G$▫ are generalized derivations ▫$F(x) = F(1)x + D(x)$▫ and ▫$G(x) = xG(1) + D(x)$▫ for all ▫$x \in \mathcal{A}$▫, where ▫$D \colon \mathcal{A} \to \mathcal{M}$▫ is a derivation. If ▫$\mathcal{A}$▫ is not generated by idempotents then there exist also nonstandard solutions for maps ▫$F$▫ and ▫$G$▫. In the case of ▫$\mathcal{A}$▫ being a triangular algebra under some condition on bimodule ▫$\mathcal{M}$▫ the characterization of maps ▫$F$▫ and ▫$G$▫ is given. We also consider conditions on algebra ▫$\mathcal{A}$▫ making it a zero product determined algebra.
    Vir: Linear algebra and its applications. - ISSN 0024-3795 (Vol. 445, 2014, str. 347-368)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2014
    Jezik - angleški
    COBISS.SI-ID - 20314120

    Povezava(-e):

    http://dx.doi.org/10.1016/j.laa.2013.12.010

Vnos na polico