Eilenberg–Niven theorem generalizes the fundamental theorem of algebra for quaternionic polynomials,¹ and this theorem was further generalized to also encompass octonionic polynomials.²

Does similar theorem holds for the sedenion algebra?

References:

[1] Eilenberg, Samuel; Niven, Ivan, The “fundamental theorem of algebra” for quaternions, Bull. Am. Math. Soc. 50, 246-248 (1944). ZBL0063.01228.

[2] Jou, Yuh-Lin, The ’fundamental theorem of algebra’ for Cayley numbers, Sci. Record, Acad. Sinica 3, 29-33 (1950). ZBL0039.26701.