On \(n\)-spaces over \(D\), \(D\) a nearfield or division algebra (Q2717909)

Let \(D\) be a nearfield or a division algebra. Let \(V\) be the Cartesian product of \(D\) with itself \(n\) times. We call \(V\) an \(n\)-space over \(D\).NEWLINENEWLINENEWLINEThe author studies \(n\)-spaces for any positive integer \(n\). In section 1 he gives basic definitions and known properties on nearfields and division algebras. Throughout section \(2 D\) is a nearfield. The results obtained by J. André are proved in a more general setting [see \textit{H. Wahling}, ``Theorie der Fastkörper'', Thales Verlag, Essen (1987)]. (Proofs are not given in Wahling's publication). For the convenience of the reader the author presents proofs in this section. In section 3 he gives similar definitions, propositions and theorems like in section 2, now \(D\) a division algebra.