(Stellenbosch : University of Stellenbosch, 2005-03) Kriel, Marelize; Green, B. W.; University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences.
The aim of this thesis is to study the unital subrings contained in associative algebras arising
as the endomorphism algebras of hyperelliptic Jacobians over finite fields.
In the first part we study associative algebras with special emphasis on maximal orders. In
the second part we introduce the theory of abelian varieties over finite fields and study the
ideal structures of their endomorphism rings.
Finally we specialize to hyperelliptic Jacobians and study their endomorphism rings.