Asymptotic Prime Divisors
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1023
Stephen McAdam
Asymptotic Prime Divisors
Springer-Verlag Berlin Heidelberg New York Tokyo 1983
Author
Stephen McAdam Department of Mathematics, University of Texas at Austin Austin, Texas 78712, USA
AMS Subject Classifications (1980): 13A17, 13E05 ISBN 3-540-12722-4 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-12722-4 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights 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. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1983 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
TO MARTHA
ACKNOWLEDCMENTS Numerous people have participated in the study of asymptotic prime divisors, and I have tried to acknowledge, in the text, a sampling of their contributions. To do so entirely would be impossible, and I hope I have been fair in my selection. Certain people have been particularly helpful to me, as much in stimulating conversations as in specific results.
I offer my gratitude to Paul Eakin, Ray Heitmann,
Dan Katz and Keith Whittington.
My special thanks goes, as it does so often, to
Jack Ratliff. Part of my research was supported by the National Science Foundation, for which I am grateful. Nita Goldrick typed the manuscript. difficult task.
Her great skill and patience eased a
TABLE OF CONTENTS Page INTRODUCTION CHAPTER I:
VIII A* (I)
B* (I)
and
1
CHAPTER II I :
A* (I) - B* (I) -« A (I)
CHAPTER IV:
A Characterization of
CHAPTER V:
Asymptotic Sequences
32
CHAPTER VI:
Asymptotic Sequences Over Ideals
42
CHAPTER VII:
Asymptotic Grade
55
CHAPTER II:
A*
--I
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