2014/01/13 by Geroldinger, Alfred, Ramacher, Sebastian, Reinhart, Andreas · 1 citation
#13A15 #13F05 #20M14 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1401.2761
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, R its complete integral closure, and suppose that the conductor \mathfrak f = (R : R) is regular. If the residue class ring R/\mathfrak f and the class group \mathcal C ( R) are both finite, then R is a C-ring. Moreover, we study both v-Marot rings and C-rings under various ring extensions.