Navin Singhi : Projective Planes

Posted by , part of the Departmental Colloquium.

At

Oct. 15, 2007, 4 p.m.

In

SEO 636

Abstract

A new class of ternary rings -- semiadditive rings -- is defined. A free semiadditive ring plays a similar role in studying planar ternary rings as the ring of integers or polynomial rings over integers play in studying fields. Methods developed recently to study free semiadditive rings will be discussed. A well known result of G. Higman on loops and its generalization to semiadditive rings will be discussed. Two well known conjectures on projective planes state that the order of every finite projective plane is a power of a prime number and that a finite projective plane with no proper subplanes is isomorphic to a plane coordinatized by a prime field. Application of the above mentioned results to these problems will be discussed.