Posner's theorem

Short description: Theorem in algebra

In algebra, Posner's theorem states that given a prime polynomial identity algebra A with center Z, the ring [math]\displaystyle{ A \otimes_Z Z_{(0)} }[/math] is a central simple algebra over [math]\displaystyle{ Z_{(0)} }[/math], the field of fractions of Z. It is named after Ed Posner.

References

• 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.