Jeudi 3 avril 2008, à 14h30 en B547.

Orateur : Zur Izhakian (LIAFA, Univ. Paris 7).

Titre : Extended Tropical Algebras - Basic Notions.

Tropical mathematics is a mathematics over the idempotent semiring (R,+,max), the real numbers equipped with the operations of maximum and summation - addition and multiplication respectively. The objective of the talk is to introduce the fundamentals of algebras defined over the extended tropical semiring - a new structure of a semiring that generalizes the former one. Despite our objects are typically combinatorial, and the ground structure is a semiring, yet, much of the classical results in real commutative algebra are carried over this structure -- matrix algebra is our main example.