On purely inseparable extensions

and their generators

Author:
D. Daigle

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1337-1345

MSC (1991):
Primary 13F20

MathSciNet review:
1327003

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Abstract: Let be a field of characteristic and a polynomial algebra in two variables. By a *-generator* of we mean an element of for which there exist and such that . We also define a *-line* of to mean any element of whose coordinate ring is that of a -generator. Then we prove that if is such that is a -line of (where is an indeterminate over ), then is a -generator of . This is analogous to the well-known fact that if is such that is a line of , then is a variable of . We also prove that if is a -line of for which there exist and such that , then is in fact a -generator of .

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Additional Information

**D. Daigle**

Affiliation:
Department of Mathematics, University of Ottawa, Ottawa, Canada K1N 6N5

Email:
daniel@zenon.mathstat.uottawa.ca

DOI:
http://dx.doi.org/10.1090/S0002-9939-96-03377-1

Received by editor(s):
June 7, 1994

Additional Notes:
The author was supported by a grant from NSERC Canada

Communicated by:
Eric M. Friedlander

Article copyright:
© Copyright 1996
American Mathematical Society