Graded division algebras over the field of real numbers

Triangulaizability of Algebras Over Division Rings

Correspondences between Valued Division Algebras and Graded Division Algebras

If D is a tame central division algebra over a Henselian valued field F , then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF . After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map ...

Hilbert Functions of Standard Graded Algebras over a Field

In this talk, we introduce Hilbert functions of a graded algebras over a field, and one of the long standing conjectures concerning them, Fröberg conjecture. Then we study relations between Fröberg conjecture on Hilbert series and Moreno-Socias Conjecture. Consequently, we show that Fröberg conjecture holds for special cases as an example. 1. Almost Reverse Lexicographic Monomial Ideal Let R = ...

triangulaizability of algebras over division rings

On the diameter of the commuting graph of the full matrix ring over the real numbers

‎In a recent paper C‎. ‎Miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{M}_n(mathbb{R})$ is equal to $4$ if either $n=3$ or $ngeq5$‎. ‎But the case $n=4$ remained open‎, ‎since the diameter could be $4$ or $5$‎. ‎In this work we close the problem showing that also in this case the diameter is $4$.