Simple subrings of algebras over fields
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- by Jan Krempa PDF
- Proc. Amer. Math. Soc. 81 (1981), 511-512 Request permission
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
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- Ring theory, Lecture Notes in Pure and Applied Mathematics, vol. 40, Marcel Dekker, Inc., New York, 1978. Edited by F. van Oystaeyen. MR 522810
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 511-512
- MSC: Primary 17A99
- DOI: https://doi.org/10.1090/S0002-9939-1981-0601718-6
- MathSciNet review: 601718