| Title:
|
Ideal class (semi)groups and atomicity in Prüfer domains (English) |
| Author:
|
Hasenauer, Richard Erwin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
891-900 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We explore the connection between atomicity in Prüfer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prüfer domains of finite character to be atomic. We construct a non-Noetherian almost Dedekind domain and exhibit a generating set for the ideal class semigroup. (English) |
| Keyword:
|
Prüfer domain |
| Keyword:
|
factorization |
| MSC:
|
13A50 |
| MSC:
|
13F15 |
| idZBL:
|
07396205 |
| idMR:
|
MR4295253 |
| DOI:
|
10.21136/CMJ.2020.0136-20 |
| . |
| Date available:
|
2021-08-02T08:10:35Z |
| Last updated:
|
2023-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149064 |
| . |
| Reference:
|
[1] Coykendall, J., Hasenauer, R. E.: Factorization in Prüfer domains.Glasg. Math. J. 60 (2018), 401-409. Zbl 1393.13013, MR 3784055, 10.1017/S0017089517000179 |
| Reference:
|
[2] Gilmer, R.: Multiplicative Ideal Theory.Queen's Papers in Pure and Applied Mathematics 90. Queen's University, Kingston (1992). Zbl 0804.13001, MR 1204267 |
| Reference:
|
[3] Hasenauer, R. E.: Normsets of almost Dedekind domains and atomicity.J. Commut. Algebra 8 (2016), 61-75. Zbl 1343.13010, MR 3482346, 10.1216/JCA-2016-8-1-61 |
| Reference:
|
[4] Loper, A.: Sequence domains and integer-valued polynomials.J. Pure Appl. Algebra 119 (1997), 185-210. Zbl 0960.13005, MR 1453219, 10.1016/S0022-4049(96)00025-4 |
| Reference:
|
[5] Olberding, B.: Factorization into radical ideals.Arithmetical Properties of Commutative Rings and Monoids Lecture Notes in Pure and Applied Mathematics 241. Chapman & Hall/CRC, Boca Raton (2005), 363-377. Zbl 1091.13002, MR 2140708, 10.1201/9781420028249.ch25 |
| . |
