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>A \otimes_Z Z_{(0)}</math> is a central simple algebra over <math>Z_{(0)}</math>, the field of fractions of ''Z''.<ref>{{harvnb|Artin|1999|loc=Theorem V. 8.1.}}</ref> It is named after Ed Posner.

==Notes== {{reflist}}

== References == *{{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}}

Category:Theorems in ring theory

{{algebra-stub}}