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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, (R, S) 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 [R, S], the set of intermediate rings.

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Acknowledgments

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

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, P.O.Box 1171, 3000, Sfax, Tunisia

    Noômen Jarboui & Manar El Islam Toumi

Authors
  1. Noômen Jarboui
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  2. Manar El Islam Toumi
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Correspondence to Noômen Jarboui.

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Communicated by Siamak Yassemi.

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Jarboui, N., El Islam Toumi, M. Characterizing Maximal Non-Mori Subrings of an Integral Domain. Bull. Malays. Math. Sci. Soc. 40, 1545–1557 (2017). https://doi.org/10.1007/s40840-015-0150-0

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  • DOI: https://doi.org/10.1007/s40840-015-0150-0

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