ON v-MAROT MORI RINGS AND C-RINGS

C-domains are defined via class semigroups, and every C- domain is a Mori domain with nonzero conductor whose complete integral closure is a Krull domain with finite class group. In order to extend the concept of C-domains to rings with zero divisors, we study v-Marot rings as generalizations of ord...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of the Korean Mathematical Society 2015, 52(1), , pp.1-21
Hauptverfasser: Geroldinger, Alfred, Ramacher, Sebastian, Reinhart, Andreas
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:C-domains are defined via class semigroups, and every C- domain is a Mori domain with nonzero conductor whose complete integral closure is a Krull domain with finite class group. In order to extend the concept of C-domains to rings with zero divisors, we study v-Marot rings as generalizations of ordinary Marot rings and investigate their theory of regular divisorial ideals. Based on this we establish a generalization of a result well-known for integral domains. Let R be a v-Marot Mori ring, R^ its complete integral closure, and suppose that the conductor f = (R : R^) is regular. If the residue class ring R/f and the class group C(R^) are both finite, then R is a C-ring. Moreover, we study both v-Marot rings and C-rings under various ring extensions. KCI Citation Count: 20
ISSN:0304-9914
2234-3008
DOI:10.4134/JKMS.2015.52.1.001