Difference between revisions 45687948 and 52605685 on enwiki

'''Driss Abouabdillah''' (or Driss Bouabdillah) is a contemporary [[Moroccan]] mathematician born in [[Meknès]] on 1 a[[April 1]], [[1948]]  . THe is a [[teacher]] of [[Aalgebra]] and [[Ggeometry]] at the [[ENS]] (higher teacher training school) of [[Rabat]].

== Contributions ==

*In G[[geometry]], he gave several characterizations of similarities as [[mappings]] that preserve [[circles]] or [[spheres]] [http://www.geocities.com/bwakeel/].
*He proposed an alternative [[axiomatic]] approach to [[Euclidean Ggeometry]] by giving an axiomatic definition of [[equipollence]]. [http://www.geocities.com/bwakeel/]
*He studied maximal sub-groups of the group of [[positive isometries]] and gave several examples of such subgroups.
*He also contributes to [[Abelian Group Theory]] and to [[Commutative Algebra]] where he gave the definition of topologically [[prüferian rings]].
*In [[Nnumber Ttheory]], he discovered the following theorem on [[antichains]] of N. ( An antichain of N, for divisibility, is a set of non nul integers such that no one is divisible by another. It is not difficult to prove that the maximal cardinality of an antichain of <math>E_{2n}</math> = {1,2,...,2n} is n).

''==Abouabdillah's Theorem.'' - ==⏎
Let c∈<math>E_{2n}</math> , c = 2<sup>k</sup>c', c' odd. Then <math>E_{2n}</math> contains an antichain of cardinality n containing c if and only if 2n < 3<sup>k+1</sup>c'.

This result constitutes a complete solution with a problem of [[Paul Erdös]] posed in 1937 in Amer.Math.Monthly 44 (1937), p.179.

== Publications ==

[1] - Topologies Linéaires Minimales Sur Un Groupe Abélien. Lecture Notes in Mathematics .1006. (Springer-Verlag). Abelian group Theory. Proceedings Honolulu 1982-83.pp 582-588.

[2] - Topologies de corps A-linéaires . Pacific journal of Mathématics. Vol.107,No.2,1983.

[3] - Sur les similitudes d'un espace euclidien, Revue de Mathématiques Spéciales (RMS) No. 7 Mars 1991.(Vuibert).

[4] - Sur les sous-groupes maximaux du groupe des isométries positives. Revue de Mathématiques de l'enseignement supérieur (RMS) Numéro 9-10. Mai-Juin 1999.(Vuibert).

[5] - Contributions en Géométrie. Monographie de cinq articles de recherche en Géométrie. Avril 2001, ISBN 9954-8096-0-0, Avril 2001.

[6] - Notions fondamentales de géométrie ; Ouvrage destiné à la préparation de l'Agrégation mathématique ; ISBN 9981-1697-2-2, Editions Dar Es-Salam ,1997.

[7] - K. Benabdallah and D. Bouabdillah. Straight and Strongly Straight Primary Modules over Principal Ideal Domains. Abelien Groups and Modules. Proceeding of The Udine Conference . April 1984.CISM Courses And Lectures No.287 Springer Verlag pp.115-130.

[8] - D. Abouabdillah & J.Turgeon, On a 1937 problem of Paul Erdös concerning certain finite sequences of integers none divisible by another. Congressus Numerantium. A conference journal on numerical themes. Vol.43, December,1984, (Winnipeg, Canada), pp.19-22.

[[Category:Moroccan mathematicians]]
[[Category:1948 births]]
[[Category:Living people]]

[[fr:Driss Abouabdillah]]