On associative division algebras

Small Non-Associative Division Algebras up to Isotopy

Assume a distributed database consisting of a large number of objects that can be created, deleted, and modified by manipulations. We want to capture the state of the system in a very small bit-string (a signature as in [2]). We now hash (map) the set of all possible manipulations into a finite, non-associative algebra. We can capture the state of an object also in a signature, an element in th...

On Nonassociative Division Algebras^)

Integrable ODEs on Associative Algebras

In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamilto-nian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential equations. We choose existence of hierarchies of first integrals and/or symmetries as a criterion for integrability and justify it by examples. Using our compo...

On normalizers of maximal subfields of division algebras

‎Here‎, ‎we investigate a conjecture posed by Amiri and Ariannejad claiming‎ ‎that if every maximal subfield of a division ring $D$ has trivial normalizer‎, ‎then $D$ is commutative‎. ‎Using Amitsur classification of‎ ‎finite subgroups of division rings‎, ‎it is essentially shown that if‎ ‎$D$ is finite dimensional over its center then it contains a maximal‎ ‎subfield with non-trivial normalize...

Triangulaizability of Algebras Over Division Rings