ON v-MAROT MORI RINGS AND C-RINGS

- Journal title : Journal of the Korean Mathematical Society
- Volume 52, Issue 1, 2015, pp.1-21
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2015.52.1.001

Title & Authors

ON v-MAROT MORI RINGS AND C-RINGS

Geroldinger, Alfred; Ramacher, Sebastian; Reinhart, Andreas;

Geroldinger, Alfred; Ramacher, Sebastian; Reinhart, Andreas;

Abstract

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, its complete integral closure, and suppose that the conductor f = (R : ) is regular. If the residue class ring R/f and the class group C() are both finite, then R is a C-ring. Moreover, we study both v-Marot rings and C-rings under various ring extensions.

Keywords

Marot rings;Mori rings;Krull rings;Krull monoids;C-rings;C-monoids;

Language

English

Cited by

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