Derivations of generalized quaternion algebra

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Kızıl E., Alagöz Y.

TURKISH JOURNAL OF MATHEMATICS, cilt.43, ss.2649-2657, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1905-86
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2649-2657
  • Anahtar Kelimeler: Derivation, quaternion, CONTROLLABILITY, SYSTEMS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

The purpose of this paper is to determine derivations of the algebra H-alpha,H-beta of generalized quaternions over the reals and hence to obtain the algebra Der(H-alpha,H-beta) of derivations of H-alpha,H-beta. Once we know derivations we might decompose Der(H-alpha,H-beta) in terms of its inner and/or central derivations whenever they exist. Apart from Der(H-alpha,H-beta) we would also be able to obtain generalized derivations, which have been studied by analysts in the context of algebras of some normed spaces, and of prime and semiprime rings.