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arXiv · 1401.2761

On v-Marot Mori rings and C-rings

Alfred Geroldinger·Sebastian Ramacher·Andreas Reinhart
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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 introduce $v$-Marot rings as generalizations of ordinary Marot rings and study 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, $\hat R$ its complete integral closure, and suppose that the conductor $\mathfrak f = (R : \hat R)$ is regular. If the residue class ring $R/\mathfrak f$ and the class group $\mathcal C (\hat R)$ are both finite, then $R$ is a C-ring. Moreover, we study both $v$-Marot rings and C-rings under various ring extensions.

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Alfred Geroldinger, Sebastian Ramacher, Andreas Reinhart. 2014-10-29. On v-Marot Mori rings and C-rings. https://arxiv.org/abs/1401.2761

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