On skew field coproducts with a finite extension
The author considers one of the most interesting constructions in skew field theory (which was introduced by him many years ago), namely the skew field coproduct. In this paper he looks at the skew field coproduct \(U\) of a skew field \(E\) which is a \(k\)-algebra with a commutative binomial extension \(F\) of \(k\), i.e. an extension given by a polynomial \(x^n-\lambda\). He shows that \(U\) can be expressed as a cyclic extension of the skew field coproduct \(K\) of \([F:k]\) copies of \(E\). As a linear space \(U\) can be also viewed as a tensor product of \(K\) with \(F\) but with more complicated multiplication. He also provides additional information on the centralizer of \(F\) in \(U\) and examines the case when \(F\) is a Galois extension.
scientific article; zbMATH DE number 997621