Abstract
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.
Citation
Pierrette Cassou-Noguès. Daniel Daigle. "Very good and very bad field generators." Kyoto J. Math. 55 (1) 187 - 218, April 2015. https://doi.org/10.1215/21562261-2848160
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