A Theorem on Division Rings

Irving Kaplansky

doi:10.4153/CJM-1951-033-7

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The object of this note is to prove the following theorem.

THEOREM. Let A be a division ring with centre Z, and suppose that for every x in A, some power (depending on x) is in . Then A is commutative.

References

[1] Hua, L. K., Some properties of a sfield, Proc. Nat. Acad. Sci. USA, vol. 35 (1949), 533–537.Google Scholar

[2] Jacobson, N., The radical and semi-simplicity for arbitrary rings, Amer. J. of Math., vol. 67 (1945), 300–320.Google Scholar

[3] Jacobson, N., Structure theory for algebraic algebras of bounded degree, Ann. of Math., vol. 46 (1945), 695–707.Google Scholar

[4] Kaplansky, I., Rings with a polynomial identity, Bull. Amer. Math. Soc, vol. 54 (1948), 575–580.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Herstein, I. N. 1953. A Theorem on Rings. Canadian Journal of Mathematics, Vol. 5, Issue. , p. 238.

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