I geometri italiani e i Grundlagen der Geometrie di Hilbert
The tropical semifield, i.e., the real numbers enhanced by the operations of addition and maximum, serves as a base of tropical mathematics. Addition is an abelian group operation, whereas the maximum defines an idempotent semigroup structure. We address the question of the geometry of idempotent semigroups, in particular, tropical algebraic sets carrying the structure of a commutative idempotent semigroup. We show that commutative idempotent semigroups are contractible, that systems of tropical...
In questa Nota costruiamo una famiglia di -archi completi di tale che , per ogni . La dimostrazione della completezza si basa sul classico Teorema di Hasse-Weil riguardante il numero dei punti di una curva algebrica irriducibile di .
The main results are the inequalities (1) and (6) for the minimal number of -structure classes,which improve the ones from [3], and also some geometrical connections, especially the inequality (13).