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  • 1.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Richter, Johan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Hom-associative Ore extensions and weak unitalizations2018In: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 24, p. 174-194Article in journal (Refereed)
    Abstract [en]

    We introduce hom-associative Ore extensions as non-unital, nonassociative Ore extensions with a hom-associative multiplication, and give some necessary and sucient conditions when such exist. Within this framework, we construct families of hom-associative quantum planes, universal enveloping algebras of a Lie algebra, and Weyl algebras, all being hom-associative generalizations of their classical counterparts, as well as prove that the latter are simple. We also provide a way of embedding any multiplicative hom-associative algebra into a multiplicative, weakly unital hom-associative algebra, which we call a weak unitalization.

  • 2.
    Richter, Johan
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Centralizers in Ore extensions over polynomial rings2014In: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 15, p. 15p. 196-207Article in journal (Refereed)
    Abstract [en]

    In this paper we consider centralizers of single elements in Ore extensions of the ring of polynomials in one variable over a field. We show that they are commutative and finitely generated as an algebra. We also show that for certain classes of elements their centralizer is singly generated as an algebra.

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