On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients

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Twistor transforms of quaternionic functions and orthogonal complex structures (2012, background): “It turns out that this algebraic structure is strictly related to the distribution of the zeros (see [12, 14, 16]).”
Slice regular functions on real alternative algebras (2010, methodology): “This estimate was improved on the quaternions by Pogorui and Shapiro [30]: if p has s spherical zeros and l non–spherical zeros, then 2s + l ≤ m. Gentili and Struppa [20] showed that, using the right definition of multiplicity, the number of zeros of p equals the degree of the polynomial.”
A new series expansion for slice regular functions (2011, background): “For this reason [12] introduced alternative notions of multiplicity for the roots of regular polynomials.”
Regular Functions of a Quaternionic Variable (2013, methodology): “For this reason [31] introduced alternative notions of multiplicity.”