Addendum to “Factoring skew polynomials over Hamilton's quaternion algebra and the complex numbers” [J. Algebra 427 (2015) 20–29] - Pumplün, S. (Journal of algebra, 2015)
Let D be the quaternion division algebra over a real closed field F. Then every non-constant polynomial in a skew-polynomial ring D[t;σ,δ] decomposes into a product of linear factors, and thus has a zero in D. This improves [8, Theorem 2].