An arithmetical characterization of finite elementary 2-groups

Authors
Chapman, ST Smith, WW
Citation
St. Chapman et Ww. Smith, An arithmetical characterization of finite elementary 2-groups, COMM ALGEB, 29(3), 2001, pp. 1249-1257
Citations number
19
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
29
Issue
3
Year of publication
2001
Pages
1249 - 1257
Database
ISI
SICI code
0092-7872(2001)29:3<1249:AACOFE>2.0.ZU;2-Y
Abstract
Beginning with Carlitz's well known characterization of algebraic number ri ngs with class number two, arithmetical characterizations of divisor class groups have been a topic of interest in the literature. In this note we dev elop a characterization of Dedekind domains with finite elementary 2-group class group. The characterization is in terms of the asymptotic behavior of the number of distinct factorizations of powers of an irreducible element.