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A weak version of Rolle's theorem
Author(s):
Thomas
C.
Craven
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3147-3153.
MSC (1991):
Primary 12D10, 12E05;
Secondary 12J10
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Abstract:
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:
- [BCP]
- R. Brown, T. Craven and M.J. Pelling, Ordered fields satisfying Rolle's theorem, Illinois J. Math 30 (1986), 66-78. MR 87f:12004
- [Co]
- S. D. Cohen, The distribution of polynomials over finite fields, Acta Arithm. 17 (1970), 255-271. MR 43:3234
- [C]
- T. Craven, Intersections of real closed fields, Canadian J. Math. 32 (1980), 431-440. MR 81i:12026
- [CC]
- T. Craven and G. Csordas, Multiplier sequences for fields, Illinois J. Math. 21 (1977), 801-817. MR 58:27921
- [K]
- I. Kaplansky, Fields and Rings, 2nd ed., University of Chicago Press, Chicago, 1972. MR 50:2139
- [R]
- P. Ribenboim, Théorie des Valuations, Les Presses de l'Université de Montréal, Montreal, Quebec, 1964/1968. MR 40:2670
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Additional Information:
Thomas
C.
Craven
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email:
tom@math.hawaii.edu
DOI:
10.1090/S0002-9939-97-03910-5
PII:
S 0002-9939(97)03910-5
Keywords:
Polynomial,
multiplier sequence,
valuation theory,
ordered field
Received by editor(s):
January 23, 1996
Received by editor(s) in revised form:
May 13, 1996
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
1997,
American Mathematical Society
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