Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON v-MAROT MORI RINGS AND C-RINGS

  • Geroldinger, Alfred (Institut fur Mathematik und Wissenschaftliches Rechnen Karl-Franzens-Universitat Graz) ;
  • Ramacher, Sebastian (Institut fur Mathematik und Wissenschaftliches Rechnen Karl-Franzens-Universitat Graz) ;
  • Reinhart, Andreas (Institut fur Mathematik und Wissenschaftliches Rechnen Karl-Franzens-Universitat Graz)
  • Received : 2013.12.14
  • Published : 2015.01.01
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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 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, $\hat{R}$ its complete integral closure, and suppose that the conductor f = (R : $\hat{R}$) is regular. If the residue class ring R/f and the class group 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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References

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