Posner's theorem
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In algebra, Posner's theorem states that given a prime polynomial identity algebra A with center Z, the ring A ⊗ Z Z ( 0 ) {\displaystyle A\otimes _{Z}Z_{(0)}} is a central simple algebra over Z ( 0 ) {\displaystyle Z_{(0)}}, the field of fractions of Z. It is named after Ed Posner.
Notes
- Artin, Michael (1999). (PDF). Chapter V.
- Formanek, Edward (1991). . Regional Conference Series in Mathematics. Vol. 78. Providence, RI: American Mathematical Society. ISBN 0-8218-0730-7. Zbl .
- Edward C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), pp. 180–183. doi: