On purely inseparable extensions and their generators
Author:
D. Daigle
Journal:
Proc. Amer. Math. Soc. 124 (1996), 13371345
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 wellknown 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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 R. Ganong, On plane curves with one place at infinity. J. Reine Angew. Math. 307/308 (1979), 173193. MR 82e:14036
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 T.T. Moh, On the classification problem of embedded lines in characteristic . Algebraic Geometry and Commutative Algebra in Honor of Masayoshi NAGATA, Kinokuniya (1987), 267279. MR 90a:14004
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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/S0002993996033771
PII:
S 00029939(96)033771
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
