Posner's theorem explained

In algebra, Posner's theorem states that given a prime polynomial identity algebra A with center Z, the ring

A ⊗ _{Z} Z _{(0)} is a central simple algebra over Z _{(0)} , the field of fractions of Z. It is named after Ed Posner.

References

• Web site: Artin. Michael. Noncommutative Rings. 1999. Chapter V.
• Book: Formanek, Edward . Edward W. Formanek

. Edward W. Formanek . The polynomial identities and invariants of n×n matrices . 0714.16001 . Regional Conference Series in Mathematics . 78 . Providence, RI . . 1991 . 0-8218-0730-7 .

• Edward C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), pp. 180–183.