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
References Artin, Michael (1999). "Noncommutative Rings" (PDF). Chapter V. Formanek, Edward (1991). The polynomial identities and invariants of n×n matrices. Regional Conference Series in Mathematics. Vol. 78. Providence, RI: American Mathematical Society. ISBN 0-8218-0730-7. Zbl 0714.16001. Edward C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), pp. 180–183. doi:10.2307/2032951