Exponents of skew polynomials.
Let \(f(x)\in\mathbb F_q[x]\) such that \(f(0)\neq 0\), where \(\mathbb F_q\) is a finite field. It is known that there exists a positive integer \(e=e(f)\) such that \(f(x)\) divides \(x^e-1\). The least such \(e\) is called the exponent of \(f(x)\). In this paper, the authors generalize this notion. Namely, they introduce and study the notion of exponent of a polynomial in an Ore extension \(\mathbb F_q[t;\theta]\), where \(\theta\) is the Frobenius automorphism of \(\mathbb F_q\).
scientific article; zbMATH DE number 6521809