Explicit construction of integral bases of radical function fields
The author determines explicit formulae for integral bases of radical extensions \(K\) of degree \(n\) over global rational function fields. He stipulates that the characteristic of the field of constants does not divide \(n\) thus avoiding wild ramification. Under that assumption he easily deduces an explicit formula for the discriminant of \(K\). Then he presents a suitable basis of \(K\) and proves by combinatorial means that it has the correct discriminant and is therefore an integral basis. In the last section he discusses the decomposition of primes in \(K\) and gives formulae for their degrees of inertia and their ramification indices.
scientific article; zbMATH DE number 5831872
scientific article