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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Simple subrings of algebras over fields


Author: Jan Krempa
Journal: Proc. Amer. Math. Soc. 81 (1981), 511-512
MSC: Primary 17A99
MathSciNet review: 601718
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Abstract: In this note we shall prove that if $ A$ is a not necessarily associative algebra over a field $ K$ and $ R$ is a simple subring of $ A$ with centroid $ F$ then $ {\dim _F}R \leqslant {\dim _K}A$.

Since we do not use polynomial identities in a proof of this result then we have obtained an affirmative answer to the 11th question from $ [2]$, posed by I. N. Herstein.


References [Enhancements On Off] (What's this?)

  • [1] Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0143793
  • [2] Ring theory, Lecture Notes in Pure and Applied Mathematics, vol. 40, Marcel Dekker, Inc., New York, 1978. Edited by F. van Oystaeyen. MR 522810

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DOI: https://doi.org/10.1090/S0002-9939-1981-0601718-6
Article copyright: © Copyright 1981 American Mathematical Society