Rational Formal Group Laws

Abstract

<p>This thesis is concerned with the general form of those one dimensional formal group laws over any field A which are given as rational functions over A. After having determined an exact expression for any rational function which is a formal group law over A, an investigation is made into the category whose objects are the rational formal group morphisms which are given by rational functions. The isomorphism classes of this category are then completely determined, and, are shown to be essentially equivalent to the classes of congruent quadratic forms over A, provided, of course, that the charactersistic of A is different from two.</p> <p>Finally, we generalize most of the results in the case of fields to the case of semi-prime rings, making a suitable definition of a rational formal group law over a semi-prime ring. In particular, we show that semi-primeness determines, and, is determined by, the general form of rational formal groups over commutative rings with unit.</p>