A weak version of Rolle’s theorem

A weak version of Rolle’s theorem
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by Thomas C. Craven PDF

Proc. Amer. Math. Soc. 125 (1997), 3147-3153 Request permission

We investigate the fields with the property that any polynomial over the field which splits in the field has a derivative which also splits.

References

Ron Brown, Thomas C. Craven, and M. J. Pelling, Ordered fields satisfying Rolle’s theorem, Illinois J. Math. 30 (1986), no. 1, 66–78. MR 822384
Stephen D. Cohen, The distribution of polynomials over finite fields, Acta Arith. 17 (1970), 255–271. MR 277501, DOI 10.4064/aa-17-3-255-271
Thomas C. Craven, Intersections of real closed fields, Canadian J. Math. 32 (1980), no. 2, 431–440. MR 571936, DOI 10.4153/CJM-1980-034-2
Thomas Craven and George Csordas, Multiplier sequences for fields, Illinois J. Math. 21 (1977), no. 4, 801–817. MR 568321
Irving Kaplansky, Fields and rings, 2nd ed., Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1972. MR 0349646
Paulo Ribenboim, Théorie des valuations, Séminaire de Mathématiques Supérieures, No. 9 (Été, vol. 1964, Les Presses de l’Université de Montréal, Montreal, Que., 1968 (French). Deuxième édition multigraphiée. MR 0249425