Posner's theorem

In algebra, Posner's theorem states that given a prime polynomial identity algebra A with center Z, the ring $A \otimes_Z Z_{(0)}$ is a central simple algebra over $Z_{(0)}$ , the field of fractions of Z.{{harvnb|Artin|1999|loc=Theorem V. 8.1.}} It is named after Ed Posner.

Notes

{{cite web|last=Artin|first=Michael|title=Noncommutative Rings|url=http://math.mit.edu/~etingof/artinnotes.pdf|year=1999|location=Chapter V}}
{{cite book | last=Formanek | first=Edward |authorlink= Edward W. Formanek | title=The polynomial identities and invariants of n×n matrices | zbl=0714.16001 | series=Regional Conference Series in Mathematics | volume=78 | location=Providence, RI | publisher=American Mathematical Society | year=1991 | isbn=0-8218-0730-7 | url=https://books.google.com/books?id=yxaqnQAACAAJ}}
Edward C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), pp. 180–183. {{doi|10.2307/2032951}}