Ideal class (semi)groups and atomicity in Prüfer domains

Richard Erwin Hasenauer

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 3, page 891-900
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Hasenauer, Richard Erwin. "Ideal class (semi)groups and atomicity in Prüfer domains." Czechoslovak Mathematical Journal 71.3 (2021): 891-900. <http://eudml.org/doc/297716>.

@article{Hasenauer2021,
abstract = {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.},
author = {Hasenauer, Richard Erwin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Prüfer domain; factorization},
language = {eng},
number = {3},
pages = {891-900},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ideal class (semi)groups and atomicity in Prüfer domains},
url = {http://eudml.org/doc/297716},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Hasenauer, Richard Erwin
TI - Ideal class (semi)groups and atomicity in Prüfer domains
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 3
SP - 891
EP - 900
AB - 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.
LA - eng
KW - Prüfer domain; factorization
UR - http://eudml.org/doc/297716
ER -

References

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  1. Coykendall, J., Hasenauer, R. E., 10.1017/S0017089517000179, Glasg. Math. J. 60 (2018), 401-409. (2018) Zbl1393.13013MR3784055DOI10.1017/S0017089517000179
  2. Gilmer, R., Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics 90. Queen's University, Kingston (1992). (1992) Zbl0804.13001MR1204267
  3. Hasenauer, R. E., 10.1216/JCA-2016-8-1-61, J. Commut. Algebra 8 (2016), 61-75. (2016) Zbl1343.13010MR3482346DOI10.1216/JCA-2016-8-1-61
  4. Loper, A., 10.1016/S0022-4049(96)00025-4, J. Pure Appl. Algebra 119 (1997), 185-210. (1997) Zbl0960.13005MR1453219DOI10.1016/S0022-4049(96)00025-4
  5. Olberding, B., 10.1201/9781420028249.ch25, Arithmetical Properties of Commutative Rings and Monoids Lecture Notes in Pure and Applied Mathematics 241. Chapman & Hall/CRC, Boca Raton (2005), 363-377. (2005) Zbl1091.13002MR2140708DOI10.1201/9781420028249.ch25

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