# AGANT SEMINAR

### (Algebraic Geometry, Algebra and Number Theory Seminar)

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__Date/Time/Room:__ Thursday, Oct 24, 2002, at 12:30 pm in 487
Pickard Hall

__Speaker:__
Minerva Cordero,
Department of Mathematics,
UTA

*``On the Semifield Planes of Order 5*^{4} and
Kernel GF(5^{2})''

**Abstract:**
A semifield is a non-associative division ring. To every semifield S,
we associate an affine plane with points the ordered pairs (a, b), where
a, b in S. The left nucleus (kernel) of S is the set of all elements s in S
such that s(a.b)=(s.a)b for every a, b in S. The order of a semifield is
the number of points in a line. In this talk, we study the semifields of
order 5^{4} and kernel GF(5^{2}). We show that there are
13 non-isomorphic semifield planes of order 5^{4} and kernel
GF(5^{2}); one is the Desarguesian plane coordinatized by
GF(5^{4}), three are coordinatized by the Generalized Twisted Fields
of Albert and 9 are p-primitive planes.