Ideal class (semi)groups and atomicity in Prüfer domains

Autor:	Richard Erwin Hasenauer
Rok vydání:	2020
Předmět:	Pure mathematics Class (set theory) Mathematics::Commutative Algebra Group (mathematics) Semigroup 010102 general mathematics Dedekind domain 01 natural sciences Order (group theory) Dedekind cut Ideal (ring theory) 0101 mathematics Finite character Mathematics
Zdroj:	Czechoslovak Mathematical Journal. 71:891-900
DOI:	10.21136/cmj.2020.0136-20
Popis:	We explore the connection between atomicity in Prufer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prufer 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::89f32e4e5b5248fea0139a4e91086b9a https://doi.org/10.21136/cmj.2020.0136-20 Zobrazit plný text záznamu