Additive Groups of Existentially Closed Rings
This is a report on work in progress on the structure of existentially closed rings and of their underlying groups. For simplicity of exposition we shall confine ourselves here to the ‘local case’, i.e., the case of Qp algebras, for a fixed prime p ; but
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ABELIAN
GROUPS
AND MODULES
PROCEEDINGS OF THE UDINE CONFERENCE UDINE APRIL 9-14, 1984
EDITED BY
R. GOBEL UNIVERSITAT ESSEN
C.METELLI-A.ORSATTI UNIVERSITA' DI PADOV A
L. SALCE UNIVERSIT A' DI UDINE
Springer-Verlag Wien GmbH
SCIENCES
VOLUME STAMPATO CON IL CONTRIBUTO DEL CONSIGLIO NAZIONALE DELLE RICERCHE- COMITATO PER LE SCIENZE MATEMATICHE
This work is subject to copyright. AII righ ts are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
© 1984 by Springer-Verlag Wien Originally published by CISM, Udine in 1984.
ISBN 978-3-211-81847-3 ISBN 978-3-7091-2814-5 (eBook) DOI 10.1007/978-3-7091-2814-5
Dedicated to Laszlo Fuchs on his 60th Birthday
PREFACE
The Udine '84 Conference on Abelian Groups and Modules fits into a by now long list of International Meetings on the subject; the recent ones: Las Cruces '76, Roma '77, Trento '80; Oberwolfacb '81, Honolulu '82; it will have a continuation in Oberwolfacb '85, and, hopefully, Perth '87. The special feature of this, as of all Italian Conferences on the subject, bas been the blending of Abelian Group Theory with Module Theory: thus supplying stimulating outlooks between bordering fields. Many of the greatest names in the subject were present. The approximately 70 participants, both attending and contributing the 11 Main Lectures (see list on page IV) and 43 Communications, provided the highest participation so far; their interest was rewarded by the wide spectrum of subjects treated, the generally good, and sometimes outstanding, quality of mathematical contributions, and the vitality witnessed by both classical and recent research trends throughout the field. Most of this appears in the present Volume; regrettably, due to the physical bound on the number of pages, we bad to make some choices: thus, except for the Main Lecturers, the number of pages allotted to each contributor was restricted and no survey article was accepted; publication was subjected to favourable reports by Referees appointed by the Editors; no contribution was accepted from non-participants. Nevertheless, we trust this Volume represents a faithful and exhaustive photograph of the state of the field as of today, and will provide many a challenging suggestion for the work oftomorrow. Last but not least, we like to recall that the Conference caught the opportunity supplied by Laszlo Fuchs' 60th birthday to throw a party in his honour, and dedicate this Volume to him: in thankful acknowledgement of the great contribution his work and presence are giving to the lively and promising state of our subject.
The Editors
ACKNOWLEDGEMENTS
The Conference on Abelian Groups and Modules held in Udine on April 9-14 1984 was organized by the Istituto di Algebra e Geometria of the Padova University and the Istituto di Matematica, Informatica e Sistemistica of the Udine University. The prestigeous location at Palazzo de
