Characterizing Maximal Non-Mori Subrings of an Integral Domain

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Abstract

The main purpose of this paper is to study maximal non-Mori subrings R of a domain S. We give characterizations of such domains in several cases. If the ring R is semilocal, (RS) is a normal pair, and R is a maximal non-Mori subring of S, we give sharp upper bounds for the number of rings and the length of chains of rings in [RS], the set of intermediate rings.

Keywords

Integral domain Valuation domain Mori domain Mori pair Intermediate ring Pullback 

Mathematics Subject Classification

Primary 13B99 13G05 13A15 Secondary 13C13 13F05 13B21 

Notes

Acknowledgments

The authors would like to thank the referee for his/her valuable suggestions.

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences of SfaxUniversity of SfaxSfaxTunisia

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