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GENERATORS OF FINITE FIELDS WITH PRESCRIBED TRACES
Part of
- Finite fields and commutative rings (number-theoretic aspects)
- General field theory
LUCAS REIS, SÁVIO RIBAS
Journal:

Journal of the Australian Mathematical Society / Volume 112 / Issue 3 / June 2022

Published online by Cambridge University Press:

27 May 2021, pp. 355-366

Print publication:

June 2022
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This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the existence of such elements. We then derive concrete existence results for a special class of intermediate extensions.

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GENERATORS OF FINITE FIELDS WITH PRESCRIBED TRACES