Urs Stammbach

We have inserted, in this edition, an extra chapter (Chapter X) entitled "Some Applications and Recent Developments." The first section of this chapter describes how homological algebra arose by abstraction from algebraic topology and how it has contributed to the knowledge of topology. The other four sections describe applications of the methods and results of homological algebra to other parts of algebra. Most of the material presented in these four sections was not available when this text was first published. Naturally, the treatments in these five sections are somewhat cursory, the intention being to give the flavor of the homo­ logical methods rather than the details of the arguments and results. We would like to express our appreciation of help received in writing Chapter X; in particular, to Ross Geoghegan and Peter Kropholler (Section 3), and to Jacques Thevenaz (Sections 4 and 5). The only other changes consist of the correction of small errors and, of course, the enlargement of the Index. Peter Hilton Binghamton, New York, USA Urs Stammbach Zurich, Switzerland Contents Preface to the Second Edition vii Introduction. . I. Modules.

We have inserted, in this edition, an extra chapter (Chapter X) entitled "Some Applications and Recent Developments." The first section of this chapter describes how homological algebra arose by abstraction from algebraic topology and how it has contributed to the knowledge of topology. The other four sections describe applications of the methods and results of homological algebra to other parts of algebra. Most of the material presented in these four sections was not available when this text was first published. Naturally, the treatments in these five sections are somewhat cursory, the intention being to give the flavor of the homo­ logical methods rather than the details of the arguments and results. We would like to express our appreciation of help received in writing Chapter X; in particular, to Ross Geoghegan and Peter Kropholler (Section 3), and to Jacques Thevenaz (Sections 4 and 5). The only other changes consist of the correction of small errors and, of course, the enlargement of the Index. Peter Hilton Binghamton, New York, USA Urs Stammbach Zurich, Switzerland Contents Preface to the Second Edition vii Introduction. . I. Modules.

Für 1994 wurde Zürich die Durchführung des Internationalen Mathematiker Kongresses anvertraut. Zürich ist damit der bisher einzige Ort, an dem diese Veranstaltung nach 1897 und 1932 bereits zum dritten Mal stattfinden kann. Dies ist kaum zufällig, denn das Fachgebiet Mathematik in Zürich war seit der Gründung der Universität und der Eidgenössischen Technischen Hochschule um die Mitte des 19. Jahrhunderts immer durch bedeutende Persönlichkeiten vertreten. Das vorliegende Buch gibt einen Überblick über die Entwicklung der Mathematik an den beiden Zürcher Hochschulen bis in die sechziger Jahre dieses Jahrhunderts hinein, wobei die personellen Aspekte im Vordergrund stehen. Der Text wird von vielen Abbildungen, darunter Porträts der meisten Mathematiker, die in Zürich tätig gewesen sind, illustriert.