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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The fundamental form of an inseparable extension

Author: Murray Gerstenhaber
Journal: Trans. Amer. Math. Soc. 227 (1977), 165-184
MSC: Primary 13B10
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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Keywords: Inseparable field extensions, high order derivations, Galois theory
Article copyright: © Copyright 1977 American Mathematical Society