Wittrings

This book is intended to give an introduction to some parts of the algebraic theory of quadratic forms. It grew out of a course, given by the first author at the University of Saarbrucken during the academic year 1971/72. This course considered ‘weak methods‘ in the theory of quadratic forms, i.e. methods, which apply to the classes of forms in the Wittring rather than to the forms themselves. In the meantime some topics of this course (cf.VIII ) have been treated in an excellent way in other books - we only mention Lam G D . The part of the course covered by the present book is the ringtheoretic approach to the structure of Wittrings in the framework of ‘abstract‘ Wittrings, based on the papers [)f[], [)!J. Working with these rings yields a greater flexibility than just working with the Wittrings of fields. Besides this the study of abstract Wittrings has the advantage, that the results are not limited to the case of Wittrings over fields, but carryover to local rings, and thus give an indespensable contribution to the local part of a theory of forms over algebraic varieties (cf. [)~ for a first impression of this theory). After having read this book, the reader will be well­ prepared to understand the local theory (cf. e. g. Q![]).