Abstract
This paper contains a self-contained, minimal computational account of Cohen's 1990 theorem that there exists a primitive element of a given finite field with arbitrary prescribed trace over a subfield. The only non-trivial exception is that there is no primitive element in the 64-element field with trace zero over the 4-element field. The original proof was deduced from a number of results on different themes, involving more computation and direct verification. Consequently, the proof is more in tune with current general approaches to the 1992 Hansen-Mullen primitivity conjecture.
Original language | English |
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Pages (from-to) | 283-300 |
Number of pages | 18 |
Journal | Southeast Asian Bulletin of Mathematics |
Volume | 29 |
Issue number | 2 |
Publication status | Published - 2005 |
Externally published | Yes |