**Contemporary Mathematics**

Volume: 102;
1989;
167 pp;
Softcover

MSC: Primary 13;

Print ISBN: 978-0-8218-5108-1

Product Code: CONM/102

List Price: $48.00

Individual Member Price: $38.40

**Electronic ISBN: 978-0-8218-7690-9
Product Code: CONM/102.E**

List Price: $48.00

Individual Member Price: $38.40

# Primes Associated to an Ideal

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*Stephen McAdam*

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 one-year 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

## Primes Associated to an Ideal

- Table of Contents xi12 free
- Preface xiii14 free
- 1. Basic Results 116 free
- 2. Examples 1934
- 3. Essential and Asymptotic sequences 2338
- 4. Schenzel's Theorems 3550
- 5. The relative Rees ring of I and J 4358
- 6. Two asymptotic functions 4964
- 7. Finite transforms 6378
- 8. Essential primes and Projective extensions 7792
- 9. Persistent primes and Projective extensions 87102
- 10. Prime divisors of principal ideals 101116
- 11. Sporadic primes 109124
- 12. Irrelevant prime divisors of uR(I) 117132
- 13. Generalizations to many ideals 125140
- 14. Grade functions 135150
- 15. Partial orderings on grade functions 149164
- References 161176
- Index 165180
- Index to symbols 167182