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On Purely Inseparable Extensions of Unbounded Exponent

Published online by Cambridge University Press:  20 November 2018

G. F. Haddix ,
J. N. Mordeson  and
B. Vinograde
G. F. Haddix
Affiliation:
Iowa State University, Ames, Iowa
J. N. Mordeson
Affiliation:
Creighton University, Omaha, Nebraska
B. Vinograde
Affiliation:
Creighton University, Omaha, Nebraska
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Let L/K be a field extension of characteristic p ≠ 0. If L/K is purely inseparable and of bounded exponent, then the property that L has a subbasis over K (11, p. 436) is of significance in the theory of higher derivations (11) and in the theory of Hopf algebras (9; 10). In this case, where L/K is of bounded exponent, it has been shown independently in (1; 9; 5) that L/K having a sub-basis is equivalent to the property that L/K is modular (9, p. 401). Our aim in this paper is to extend and apply these properties for L/K purely inseparable and of unbounded exponent.

In Theorem 1, we give several conditions on a p-basis of L which are equivalent to the property that L/K has a sub-basis. In Theorem 2, we give a sequence of implications starting with L/K has a sub-basis.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1526 - 1532
Copyright
Copyright © Canadian Mathematical Society 1969

References

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