Factorization in integral domains:
Based on the recent proceedings of the University of Iowa's Conference on Factorization in Integral Domains and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City, this outstanding volume gathers, for the first time in a si...
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1997
|
| Schriftenreihe: | Lecture notes in pure and applied mathematics
189 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Based on the recent proceedings of the University of Iowa's Conference on Factorization in Integral Domains and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City, this outstanding volume gathers, for the first time in a single source, current work on factorization in integral domains and monoids and the theory of divisibility - emphasizing possible different lengths of factorizations into irreducible elements Including a diverse range of commutative ring theory topics, such as Prufer domains, one-dimensional Noetherian rings, Henselian pullbacks, intersections of prime ideals, integral and complete integral closures, stable ideals and prime ideals in polynomial rings, and the genus class group, Factorization in Integral Domains surveys elasticity...the catenary and tame degrees...the role of monoid-theoretic techniques involving divisor theory and block monoids ...applications of Krull and block monoids to studies of factorization in integral domains... up-to-date results on integral domains with a finite number of nonassociate atoms, with finitely generated groups of divisibility, and integral domains whose monoids of fractional ideals are finitely generated...and more Written by leading mathematicians representing institutions in the United States, Europe, and the Middle East, Factorization in Integral Domains is an excellent resource for commutative ring theorists, algebraic number theorists, and graduate students in these disciplines |
| Beschreibung: | X, 432 S. |
| ISBN: | 0824700325 |
Internformat
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| 490 | 1 | |a Lecture notes in pure and applied mathematics |v 189 | |
| 520 | 3 | |a Based on the recent proceedings of the University of Iowa's Conference on Factorization in Integral Domains and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City, this outstanding volume gathers, for the first time in a single source, current work on factorization in integral domains and monoids and the theory of divisibility - emphasizing possible different lengths of factorizations into irreducible elements | |
| 520 | |a Including a diverse range of commutative ring theory topics, such as Prufer domains, one-dimensional Noetherian rings, Henselian pullbacks, intersections of prime ideals, integral and complete integral closures, stable ideals and prime ideals in polynomial rings, and the genus class group, Factorization in Integral Domains surveys elasticity...the catenary and tame degrees...the role of monoid-theoretic techniques involving divisor theory and block monoids ...applications of Krull and block monoids to studies of factorization in integral domains... up-to-date results on integral domains with a finite number of nonassociate atoms, with finitely generated groups of divisibility, and integral domains whose monoids of fractional ideals are finitely generated...and more | ||
| 520 | |a Written by leading mathematicians representing institutions in the United States, Europe, and the Middle East, Factorization in Integral Domains is an excellent resource for commutative ring theorists, algebraic number theorists, and graduate students in these disciplines | ||
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Datensatz im Suchindex
| _version_ | 1804125957066326016 |
|---|---|
| adam_text | Contents
Preface Hi
Contributors vii
1. Elasticity of Factorizations in Integral Domains: A Survey 1
David F. Anderson
2. Finitely Generated Monoids, Finitely Primary Monoids, and
Factorization Properties of Integral Domains 31
Franz Halter Koch
3. Krull Domains and Monoids, Their Sets of Lengths, and Associated
Combinatorial Problems 73
Scott Chapman and Alfred Geroldinger
4. The Catenary Degree and Tameness of Factorizations in
Weakly Krull Domains 113
Alfred Geroldinger
5. The Theory of Divisibility 155
Joe Mott
6. Some Generalizations of GCD Domains 189
D. D. Anderson and Roy Quintero
1. Factorization in Commutative Rings with Zero Divisors, II 197
D. D. Anderson and Silvia Valdes Leon
8. On r Invertibility, IV 221
D. D. Anderson and Muhammad Zafrullah
9. Factorization in Subrings of K[X] or K[[X]] 227
David F. Anderson and Jaenam Park
v
vi Contents
10. Factorization in K[[S]] 243
David F. Anderson and Janice Winner
11. Invariant Theory in Characteristic p: Hazlett s Symbolic Method
for Binary Quantics 257
Joseph P. Brennan
12. A Basis for the Ring of Polynomials Integer Valued on Prime Numbers 271
Jean Luc Chabert, Scott Chapman, and William W. Smith
13. Factorization of Bonds and Other Cash Flows 285
Douglas L. Costa
14. A Characterization of Polynomial Rings with the Half Factorial Property 291
Jim Coykendall
15. On Characterizations of Priifer Domains Using Polynomials
with Unit Content 295
David E. Dobbs
16. On Flat Divided Prime Ideals 305
David E. Dobbs
17. On Henselian Pullbacks 317
David E. Dobbs
18. An Intersection Condition for Prime Ideals 327
Robert Gilmer
19. Genus Class Groups and Separable Base Change 333
Robert Guralnick and Roger Wiegand
20. Generalized Integral Closures 349
Franz Halter Koch
21. Coefficient and Stable Ideals in Polynomial Rings 359
William Heinzer and David Lantz
22. Almost Generalized GCD Domains 371
Rebecca L. Lewin
23. Polynomial Behavior of Prime Ideals in Polynomial Rings and
the Projective Line Over Z 383
Aihua Li and Sylvia Wiegand
24. Characterizing When R(X) is Completely Integrally Closed 401
Thomas G. Lucas
Contents vii
25. On Root Closure in Noetherian Domains 417
Moshe Roitman
Index 429
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| id | DE-604.BV011440333 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:09:48Z |
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| isbn | 0824700325 |
| language | English |
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| series | Lecture notes in pure and applied mathematics |
| series2 | Lecture notes in pure and applied mathematics |
| spelling | Factorization in integral domains ed. by Daniel D. Anderson New York [u.a.] Dekker 1997 X, 432 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in pure and applied mathematics 189 Based on the recent proceedings of the University of Iowa's Conference on Factorization in Integral Domains and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City, this outstanding volume gathers, for the first time in a single source, current work on factorization in integral domains and monoids and the theory of divisibility - emphasizing possible different lengths of factorizations into irreducible elements Including a diverse range of commutative ring theory topics, such as Prufer domains, one-dimensional Noetherian rings, Henselian pullbacks, intersections of prime ideals, integral and complete integral closures, stable ideals and prime ideals in polynomial rings, and the genus class group, Factorization in Integral Domains surveys elasticity...the catenary and tame degrees...the role of monoid-theoretic techniques involving divisor theory and block monoids ...applications of Krull and block monoids to studies of factorization in integral domains... up-to-date results on integral domains with a finite number of nonassociate atoms, with finitely generated groups of divisibility, and integral domains whose monoids of fractional ideals are finitely generated...and more Written by leading mathematicians representing institutions in the United States, Europe, and the Middle East, Factorization in Integral Domains is an excellent resource for commutative ring theorists, algebraic number theorists, and graduate students in these disciplines Anneaux commutatifs - Congrès ram Factorisation (Mathématiques) - Congrès ram Commutative rings Congresses Factorization (Mathematics) Congresses Integral domains Congresses Faktorisierung (DE-588)4128927-4 gnd rswk-swf Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Integritätsbereich (DE-588)4266311-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1996 Iowa City Iowa gnd-content Kommutativer Ring (DE-588)4164825-0 s DE-604 Integritätsbereich (DE-588)4266311-8 s Faktorisierung (DE-588)4128927-4 s Anderson, Daniel D. Sonstige oth Lecture notes in pure and applied mathematics 189 (DE-604)BV005871364 189 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007694342&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Factorization in integral domains Lecture notes in pure and applied mathematics Anneaux commutatifs - Congrès ram Factorisation (Mathématiques) - Congrès ram Commutative rings Congresses Factorization (Mathematics) Congresses Integral domains Congresses Faktorisierung (DE-588)4128927-4 gnd Kommutativer Ring (DE-588)4164825-0 gnd Integritätsbereich (DE-588)4266311-8 gnd |
| subject_GND | (DE-588)4128927-4 (DE-588)4164825-0 (DE-588)4266311-8 (DE-588)1071861417 |
| title | Factorization in integral domains |
| title_auth | Factorization in integral domains |
| title_exact_search | Factorization in integral domains |
| title_full | Factorization in integral domains ed. by Daniel D. Anderson |
| title_fullStr | Factorization in integral domains ed. by Daniel D. Anderson |
| title_full_unstemmed | Factorization in integral domains ed. by Daniel D. Anderson |
| title_short | Factorization in integral domains |
| title_sort | factorization in integral domains |
| topic | Anneaux commutatifs - Congrès ram Factorisation (Mathématiques) - Congrès ram Commutative rings Congresses Factorization (Mathematics) Congresses Integral domains Congresses Faktorisierung (DE-588)4128927-4 gnd Kommutativer Ring (DE-588)4164825-0 gnd Integritätsbereich (DE-588)4266311-8 gnd |
| topic_facet | Anneaux commutatifs - Congrès Factorisation (Mathématiques) - Congrès Commutative rings Congresses Factorization (Mathematics) Congresses Integral domains Congresses Faktorisierung Kommutativer Ring Integritätsbereich Konferenzschrift 1996 Iowa City Iowa |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007694342&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT andersondanield factorizationinintegraldomains |