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Posner's theorem

In algebra, Posner's theorem states that given a prime polynomial identity algebra A with center Z, the ring is a central simple algebra over , the field of fractions of Z. It is named after Ed Posner.

Last revised

Jul 30, 2026

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Source

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.¹ It is named after Ed Posner.

Notes

Notes

Artin 1999, Theorem V. 8.1.

References

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