## LSU Historical Dissertations and Theses

1989

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Mathematics

Robert V. Perlis

#### Abstract

In 1932, E. Witt showed how the collection of bilinear forms over a field $E$ can be made into a ring called the Witt ring, $W(E)$, of $E$. Properties of bilinear forms over a field often are reflected in the algebraic properties of its Witt ring. Perlis, Szymiczek, and Conner give criteria for global fields to be Witt equivalent; that is, to have isomorphic Witt rings. We refine these criteria to obtain finite, necessary and sufficient conditions to insure Witt equivalence of number fields. These conditions yield several finiteness statements for forms over number fields. Among them, for a fixed degree $n$ $\in$ $\rm I\!N$, the number of Witt equivalence classes of number fields of degree $n$ is finite.

75

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