Journal of the Korean Mathematical Society
( Vol.52 NO.1 / 2015 )
Title
On $v$-Marot Mori rings and C-rings(ENG)
Author
Alfred Geroldinger ,Sebastian Ramacher ,Andreas Reinhart 
MSC
13F05, 13A15, 20M14
Publication
Page
1-21 Page
Abstract
Own Status
Keyword
Marot rings, Mori rings, Krull rings, Krull monoids, C-rings, C-monoids
Note
Summary
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, $widehat R$ its complete integral closure, and suppose that the conductor $mathfrak f = (R : widehat R)$ is regular. If the residue class ring $R/mathfrak f$ and the class group $mathcal C (widehat R)$ 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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