| 11. | The normal closure of any of these extensions is the full splitting field of " p ".
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| 12. | The project titles alone were deliciously impenetrable : " Polynomial Automorphisms of Splitting Fields, " for one.
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| 13. | Where is the leading coefficient and are the roots ( counting multiplicity ) of the polynomial in some splitting field.
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| 14. | Secondly supposing we consider a splitting field in which the roots of " h ( x ) " exist.
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| 15. | Fourth prize went to Davesh Maulik of Roslyn for an algebra project titled " Polynomial Automorphisms of Splitting Fields ."
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| 16. | In fact, if is an irreducible factor over of, its degree divides, as its splitting field is contained in.
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| 17. | The product formula involving the roots remains valid; the roots have to be taken in some splitting field of the polynomial.
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| 18. | From the time of Galois, the role of primitive elements had been to represent a splitting field as generated by a single element.
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| 19. | By iterating the above construction, one can construct a splitting field of any polynomial from " K " [ " X " ].
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| 20. | Now \ mathbb Z _ { p ^ r } is the ring in question and the roots must lie in the splitting field hence my last question.
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