1. Generalized Derivations and Generalized Jordan Derivations of Quaternion Rings
- Author
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Hoger Ghahramani, M. N. Ghosseiriand, and L. Heidari Zadeh
- Subjects
Ring (mathematics) ,Pure mathematics ,Mathematics::Commutative Algebra ,General Mathematics ,Unital ,010102 general mathematics ,General Physics and Astronomy ,010103 numerical & computational mathematics ,General Chemistry ,Center (group theory) ,01 natural sciences ,law.invention ,Matrix (mathematics) ,Invertible matrix ,law ,General Earth and Planetary Sciences ,0101 mathematics ,General Agricultural and Biological Sciences ,Quaternion ,Mathematics - Abstract
Let S be a unital ring in which 2 is invertible, and let $$R=H(S)$$ be the quaternion ring over S. In this paper, we characterize the generalized derivations of R and show that every generalized Jordan derivation on R is a generalized derivation. We also consider the question when a derivation (generalized derivation) of a quaternion ring is an inner derivation (generalized inner derivation). In addition, we show that the structures of the center, ideals, and the above-mentioned derivations of the quaternion rings and matrix rings are similar.
- Published
- 2021
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