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\textsc{Algebra}
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\textsc{Seminar}
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\textit{On indecomposable division algebras of exponent 2}
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A. S. Sivatski\par
St. Petersburg Electrotechnical University
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\textbf{Abstract:} For any $n > 2$, we construct central division algebras of exponent 2 and index $2^n$ over a field $E$, which are indecomposable over any odd degree extension of $E$ and which are sums of $n + 1$ quaternion algebras in the Brauer group of $E$. The construction also allows to prove that any multiquadratic extension of degree $2^{n-1}$ over a field $K$ becomes nonexcellent (in the sense of the theory of quadratic forms) when $K$ is replaced
by a suitable field extension.\vspace{\fill}
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Tuesday, October 30, 2007, 4:00 pm\par
Mathematics and Science Center: W302
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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