On Asano's theorem

EROĞLU M. P., Lee T., Lin J.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.18, sa.10, 2019 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 10
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1142/s0219498819501810
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Division algebra, invariant subspace, inner automorphism, Lie ideal, multiplicative (additive) commutator
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Let D be a division algebra over an infinite field K such that every element of D is a sum of finitely many algebraic elements. As a generalization of Asano's theorem, it is proved that every noncentral subspace of D invariant under all inner automorphisms induced by algebraic elements contains [D, D], the additive subgroup of D generated by all additive commutators of D. Flom the viewpoint we study the existence of normal bases of certain subspaces of division algebras. It is proved among other things that D is generated by multiplicative commutators as a vector space over the center of D.