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Transactions of the American Mathematical Society

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The fundamental form of an inseparable extension


Author: Murray Gerstenhaber
Journal: Trans. Amer. Math. Soc. 227 (1977), 165-184
MSC: Primary 13B10
DOI: https://doi.org/10.1090/S0002-9947-1977-0429861-9
MathSciNet review: 0429861
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Abstract: If K is a finite purely inseparable extension of a field k, then the symmetric multiderivations of K (symmetric maps $ f:K \times \cdots \times K\;(n\;{\text{times}}) \to K$ which are derivations as functions of each single variable) form a ring under the symmetrized cup product. This ring contains an element $ \Gamma (K/k)$ called the fundamental form of K over k, which is defined up to multiplication by a nonzero element of K and has the property that if B is any intermediate field between K and k, then $ \Gamma (K/B)$ divides $ \Gamma (K/k)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0429861-9
Keywords: Inseparable field extensions, high order derivations, Galois theory
Article copyright: © Copyright 1977 American Mathematical Society

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