Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 55, Number 1 (2015), 187-218.
Very good and very bad field generators
Let be a field. A field generator is a polynomial satisfying for some . If can be chosen in , we call a good field generator; otherwise, is a bad field generator. These notions were first studied by Abhyankar, Jan, and Russell in the 1970s. The present paper introduces and studies the notions of “very good” and “very bad” field generators. We give theoretical results as well as new examples of bad and very bad field generators.
Kyoto J. Math., Volume 55, Number 1 (2015), 187-218.
First available in Project Euclid: 13 March 2015
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Cassou-Noguès, Pierrette; Daigle, Daniel. Very good and very bad field generators. Kyoto J. Math. 55 (2015), no. 1, 187--218. doi:10.1215/21562261-2848160. https://projecteuclid.org/euclid.kjm/1426252135