ON v-MAROT MORI RINGS AND C-RINGS

Title & Authors
ON v-MAROT MORI RINGS AND C-RINGS
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, $\small{\hat{R}}$ its complete integral closure, and suppose that the conductor f = (R : $\small{\hat{R}}$) is regular. If the residue class ring R/f and the class group C($\small{\hat{R}}$) 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
1.
Arithmetic of seminormal weakly Krull monoids and domains, Journal of Algebra, 2015, 444, 201
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