Contemporary Mathematics 1989; 167 pp; softcover Volume: 102 ISBN10: 082185108X ISBN13: 9780821851081 List Price: US$48 Member Price: US$38.40 Order Code: CONM/102
 This book discusses five closely related sets of prime ideals associated to an ideal \(I\) in a Noetherian ring: the persistent, asymptotic, quintasymptotic, essential, and quintessential primes of \(I\). Since the appearance of the author's last book on this subject, which focused on the first two of these prime ideals, the other three sets were developed and new results were obtained for the first two. Current results are scattered over some three dozen papers, making it difficult for interested readers to become familiar with the subject. The aim of this book is to present in an efficient way the most important and interesting ideas in the subject and to show how these prime ideals reveal information about both \(I\) and the ring. Because the required background consists of little more than a standard oneyear course in commutative ring theory, the book should be acccessible to graduate students. The work is primarily intended for commutative ring theorists, but noncommutative ring theorists and algebraic geometers may also find it of interest. Table of Contents  Contents
 Basic results
 Examples
 Essential and asymptotic sequences
 Schenzel's theorems
 The relative Rees ring of \(I\) and \(J\)
 Two asymptotic functions
 Finite transforms
 Essential primes and projective extensions
 Persistent primes and projective extensions
 Prime divisors of principal ideals
 Sporadic primes
 Irrelevant prime divisors of \(uR(I)\)
 Generalizations to many ideals
 Grad functions
 Partial orderings on grade functions
