The study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement. This book presents the proceedings of two recent meetings that gathered key researchers from around the world to review recent major results. The first seven chapters demonstrate the diversity of approaches taken in studying nonunique factorizations and serve both as an introduction to factorization theory and as a survey of current trends and results. The remaining chapters reflect research motivated by arithmetical properties of commutative rings and monoids.
| Preface |
|
xi | |
| Contributors |
|
xv | |
|
Non-Atomic Unique Factorization in Integral Domains |
|
|
1 | (21) |
|
|
|
Divisibility Properties in Graded Integral Domains |
|
|
22 | (24) |
|
|
|
Extensions of Half-Factorial Domains: A Survey |
|
|
46 | (25) |
|
|
|
C-Monoids and Congruence Monoids in Krull Domains |
|
|
71 | (28) |
|
|
|
Monotone Chains of Factorizations in C-Monoids |
|
|
99 | (15) |
|
|
|
|
|
Transfer Principles in the Theory of Non-unique Factorizations |
|
|
114 | (28) |
|
|
|
|
|
Cale Monoids, Cale Domains, and Cale Varieties |
|
|
142 | (30) |
|
|
|
|
|
Weakly Krull Inside Factorial Domains |
|
|
172 | (8) |
|
|
|
|
|
|
|
The m-Complement of a Multiplicative Set |
|
|
180 | (8) |
|
|
|
|
|
Some Remarks on Infinite Products |
|
|
188 | (10) |
|
|
|
Rings with Prime Nilradical |
|
|
198 | (15) |
|
|
|
|
|
On the Ideal Generated by the Values of a Polynomial |
|
|
213 | (13) |
|
|
|
|
|
Using Factorizations to Prove a Partition Identity |
|
|
226 | (7) |
|
|
|
|
|
On Inside Factorial Integral Domains |
|
|
233 | (20) |
|
|
|
|
|
Martine Picavet-L'Hermitte |
|
|
Polynomial Separation of Points in Algebras |
|
|
253 | (7) |
|
|
|
k-Factorized Elements in Telescopic Numerical Semigroups |
|
|
260 | (12) |
|
|
|
|
|
|
|
Prufer Conditions in Rings with Zero-Divisors |
|
|
272 | (10) |
|
|
|
Unmixedness and the Generalized Principal Ideal Theorem |
|
|
282 | (11) |
|
|
|
A Note on Sets of Lengths of Powers of Elements of Finitely Generated Monoids |
|
|
293 | (11) |
|
|
|
|
|
304 | (12) |
|
|
|
|
|
On Local Half-Factorial Orders |
|
|
316 | (9) |
|
|
|
On Factorization in Krull Domains with Divisor Class Group Z2k |
|
|
325 | (12) |
|
|
|
|
|
337 | (19) |
|
|
|
A Special Type of Invertible Ideal |
|
|
356 | (7) |
|
|
|
|
|
Factorization into Radical Ideals |
|
|
363 | (15) |
|
|
|
|
|
378 | (11) |
|
|
|
|
|
|
| Index |
|
389 | |
Scott T. Chapman, Trinity University, San Antonio, Texas, U.S.A
Rohkem infot Taylor & Francis e-raamatute kohta