Van der Waerdens construction of a splitting eld
نویسنده
چکیده
In his classic book, Modern Algebra, van der Waerden gave a procedure for factoring polynomials over a nite-dimensional, separable, simple extension eld. I believe that there is a nonconstructive component to his proof, and I will indicate where it comes in and why. Although Im sure that this component could be avoided while staying within the framework that he set down, it is simpler to get around the problem by working with a splitting algebra, which is easily constructed for any polynomial and base eld. The existence of a splitting eld then follows from van der Waerdens argument.
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