Journal of the Korean Mathematical Society
( Vol.52 NO.1 / 2015 )



Title 


On $v$Marot Mori rings and Crings(ENG) 


Author 


Alfred Geroldinger ,Sebastian Ramacher ,Andreas Reinhart 


MSC 


13F05, 13A15, 20M14 


Publication 





Page 


121 Page 


Abstract 





Own Status 





Keyword 


Marot rings, Mori rings, Krull rings, Krull monoids, Crings, Cmonoids 


Note 





Summary 


Cdomains are defined via class semigroups, and every Cdomain 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 Cdomains 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 wellknown 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 Cring. Moreover, we study both $v$Marot rings and Crings under various ring extensions. 


Attach 


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