Geodesic
Polynomials with Coefficients from a Division Ring
Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 509-515

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be any division ring and let 1 be a polynomial, in the indeterminate X, with coefficients in R. Note that the powers of X are always to the right of the coefficients. We denote the set of all such polynomials by R[X].B. Beck [3] proved the following theorem for the generalized quaternion division algebra; i.e., any division ring of dimension 4 over its center:THEOREM 1. If f(X) is of degree n then f(X) has either infinitely many or at most n zeros in R.Under a reasonable definition of multiplicity Beck also proved:THEOREM 2. Let (c 1, c 2, ..., cn ) be a set of pairwise non-conjugate elements of R, and (m 1, ..., mN ) positive integers such that Σmi = n = deg f(x). 
Bray, Una; Whaples, George. Polynomials with Coefficients from a Division Ring. Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 509-515. doi: 10.4153/CJM-1983-028-1
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