Reduced simple Jordan algebras of degree three over a field with a discrete valuation
Let \(k\) be a complete discrete valuation field, \(\tilde k\) its residue class field. The author obtains necessary and sufficient conditions for isomorphism of reduced central simple Jordan algebras of degree three over \(k\) in terms of \(\tilde k\) data, assuming the absence of certain pathologies which may occur if \(\tilde k\) is of characteristic two. \textit{T. A. Springer}'s first and second residue forms [Nederl. Akad. Wet., Proc., Ser. A 58, 352--362 (1955; Zbl 0067.27605)] and the author's results on composition algebras over \(k\) [J. Algebra 29, 414--426 (1974; Zbl 0291.17013)] are used to study the quadratic forms \(T(x^\sharp)\) in Springer's criterion on isomorphism [the reviewer, Trans. Am. Math. Soc. 164, 93--103 (1972; Zbl 0236.17007)].
scientific article; zbMATH DE number 3544235