# Cyclic semirings with idempotent noncommutative addition

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Let F be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive element $$\alpha \in {F_{{q^n}}}$$ such that Î± + Î± is also primitive or Î± + Î± is primitive and Î± is a normal element...

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