O kvaternionech. [I.]
O kvaternionech. [II.]
O kvaternionech. [III.]
On ordered division rings
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel’s axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under for nonzero , instead of requiring that positive elements have a positive product. In this work, this type of ordering is studied in the case of a division ring. It is shown that it actually behaves the same as in the commutative...
On the ...-invariant for quadratics forms and the linkage of cyclic algebras.
On the roots of polynomials over division algebras.
Ostrwoski's theorem for Henselian valued skew fields.
Polynomials and degrees of maps in real normed algebras
Let be the algebra of quaternions or octonions . In this manuscript an elementary proof is given, based on ideas of Cauchy and D’Alembert, of the fact that an ordinary polynomial has a root in . As a consequence, the Jacobian determinant is always non-negative in . Moreover, using the idea of the topological degree we show that a regular polynomial over has also a root in . Finally, utilizing multiplication () in , we prove various results on the topological degree of products...
Polynomials and Vandermonde matrices over the field of quaternions.
Representation theory of local division algebras.
Schiefkörper über diskret bewerteten Körpern.
Severi-Brauer varieties of semidirect product algebras.
Skew fields of noncommutative rational functions (preliminary version)
Subgroups of finite index in an additive group of a ring.
Sums of Squares in Central Simple Algebras.
Sums of Squares in Division Algebras.
The level of cyclic division algebras.
Theorie der goniometrischen und der longimetrischen Quaternionen [Book]
Über die Existenz maximaler algebraischer Körperweiterungen.
Uniform distribution of Hasse invariants.