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Products of traceless and semi-traceless matrices over division rings and their applications
Preview AbstractIn this paper, we prove that every matrix over a division ring is representable as a product of at most 10 traceless matrices as well as a product of at most four semi-traceless matrices. By applying this result and the obtained so far other results, we show that elements of some algebras possess some rather interesting and nontrivial decompositions into products of images of non-commutative polynomials.
QUELQUES TENTATIVES DE DÉFINIR UNE NOTION GÉNÉRALE DE GROUPES ET DE CORPS DE DIMENSION UN ET DE DÉTERMINER LEURS PROPRIÉTÉS ALGÉBRIQUES
Preview AbstractWe make some attempts to define a general notion of groups and fields of dimension one, and to determine their algebraic properties.
On self-force for particles coupled to higher-order electrodynamics and scalar fields
Preview AbstractWe address the question of point particle motion coupled to classical fields, in the context of scalar fields derived from higher-order Lagrangians and BLTP electrodynamics.