ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 17, 46, 54 N. El Yacoubi, Universit Mohamed V, Rabat, Maroc. J-Generalized topological divisors of zero in topological Jordan algebras By introducing the notion of generalized topological divisors of zero in a topological Jordan algebra ([1]) (short J-g. t. d. z.), we prove that a complex and complete locally multiplicatively convex algebra possesses J-g. t. d. z. or is isomorphic to ∀. The problem is still open for a topological Jordan algebra. Nevertheless, we obtain that a complex and complete Jdivision topological Jordan algebra A either possesses J-g. t. d. z. or is isomorphic to ∀. When A is a real algebra thus A either possesses J-g. t. d. z. or is quadratic, in this last case A can be of infinite dimentional which is an essential difference with the associative case ([2]). ([1]) N. El Yacoubi, Théorèmes de structure dalgèbres de Jordan topologiques ou bornologiques , à paraître dans Algebras, Groups and Geometries. Vol.15, 1998. ([2]) N. El Yacoubi and H. Kemmoun, Jdiviseurs topologiques de zéro dans les algb̀res de Jordan p-normées unitaires , à paraître dans Periodica Mathematica Hungarica, 1998. Reference : N. El Yacoubi and H. Kemmoun, article soumis pour publication.