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Existence of Non-Trivial Deformations of Inseparable Algebraic Extension Fields II*

Published online by Cambridge University Press:  22 January 2016

Hiroshi Kimura
Hiroshi Kimura*
Affiliation:
Nagoya University
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Let K be an extension of a field k, and p denotes the characteristic. It was proved by M. Gerstenhaber ([1]) that if K is separable over k, then it is rigid and it was conjectured in [1] that, if K is not separable over k, then it is not rigid. We studied in [4] the above conjecture in certain special case. In this note we shall extend the results of [4] to inseparable algebraic extension fields.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 237 - 245
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

Footnotes

*

This work was supported by The Sakkokai Foundation.

References

[1] Gerstenhaber, M.: On the deformation of rings and algebras, Ann. of Math. 79 (1964), 59–103.CrossRefGoogle Scholar
[2] Harrison, D.K.: Commutative algebras and cohomology, Trans. Amer. Math. Soc., 104 (1962), 191–204.CrossRefGoogle Scholar
[3] Jacobsen, N.: Lectures in abstract algebra III, Van Nastrand, 1964.CrossRefGoogle Scholar
[4] Kimura, H.: Existence of non-trivial deformations of some inseparable extension fields, Nagoya Math. J. 31 (1968), 37–40.Google Scholar