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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the triviality of homogeneous algebras over an algebraically closed field
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by Lowell Sweet PDF
Proc. Amer. Math. Soc. 48 (1975), 321-324 Request permission

Abstract:

Let $A$ be a finite-dimensional algebra (not necessarily associative) over a field $K$. Then $A$ is said to be homogeneous if $\operatorname {Aut} (A)$ acts transitively on the one-dimensional subspaces of $A$. If $A$ is homogeneous and $K$ is algebraically closed, then it is shown that either ${A^2} = 0$ or $\dim A = 1$.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 321-324
  • MSC: Primary 17E05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0364382-7
  • MathSciNet review: 0364382