| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910438153403321 |
|
|
Autore |
Fontana Marco |
|
|
Titolo |
Factoring ideals in integral domains / / Marco Fontana, Evan Houston, Thomas Lucas |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
New York, : Springer, 2013 |
|
|
|
|
|
|
|
ISBN |
|
1-283-63150-4 |
9786613943958 |
3-642-31712-X |
|
|
|
|
|
|
|
|
Edizione |
[1st ed. 2013.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (169 p.) |
|
|
|
|
|
|
Collana |
|
Lecture notes of the Unione Matematica Italiana, , 1862-9113 ; ; 14 |
|
|
|
|
|
|
Altri autori (Persone) |
|
HoustonEvan <1948-> |
LucasTom (Thomas) |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Description based upon print version of record. |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references and index. |
|
|
|
|
|
|
Nota di contenuto |
|
Factoring Ideals in Integral Domains; Preface; Contents; Chapter 1 Introduction; Chapter 2 Sharpness and Trace Properties; 2.1 h-Local Domains; 2.2 Sharp and Double Sharp Domains; 2.3 Sharp and Antesharp Primes; 2.4 Trace Properties; 2.5 Sharp Primes and Intersections; Chapter 3 Factoring Ideals in Almost Dedekind Domains and Generalized Dedekind Domains; 3.1 Factoring with Radical Ideals; 3.2 Factoring Families for Almost Dedekind Domains; 3.3 Factoring Divisorial Ideals in Generalized Dedekind Domains; 3.4 Constructing Almost Dedekind Domains |
Chapter 4 Weak, Strong and Very Strong Factorization4.1 History; 4.2 Weak Factorization; 4.3 Overrings and Weak Factorization; 4.4 Finite Divisorial Closure; Chapter 5 Pseudo-Dedekind and Strong Pseudo-Dedekind Factorization; 5.1 Pseudo-Dedekind Factorization; 5.2 Local Domains with Pseudo-Dedekind Factorization; 5.3 Strong Pseudo-Dedekind Factorization; 5.4 Factorization and the Ring R(X); Chapter 6 Factorization and Intersections of Overrings; 6.1 h-Local Maximal Ideals; 6.2 Independent Pairs of Overrings; 6.3 Jaffard Families and Matlis Partitions; 6.4 Factorization Examples |
Symbols and DefinitionsReferences; Index |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
This volume provides a wide-ranging survey of, and many new results |
|
|
|
|
|
|
|
|
|
|
on, various important types of ideal factorization actively investigated by several authors in recent years. Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals. Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well. |
|
|
|
|
|
| |