Posner's theorem

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Short description: Theorem in algebra

In algebra, Posner's theorem states that given a prime polynomial identity algebra A with center Z, the ring AZZ(0) is a central simple algebra over Z(0), the field of fractions of Z.[1] It is named after Ed Posner.

References

  1. Artin 1999, Theorem V. 8.1.
  • Artin, Michael (1999). "Noncommutative Rings". Chapter V. http://math.mit.edu/~etingof/artinnotes.pdf. 
  • Formanek, Edward (1991). The polynomial identities and invariants of n×n matrices. Regional Conference Series in Mathematics. 78. Providence, RI: American Mathematical Society. ISBN 0-8218-0730-7. 
  • Edward C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), pp. 180–183.