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