Korean J. Math. Vol. 22 No. 3 (2014) pp.455-462
DOI: https://doi.org/10.11568/kjm.2014.22.3.455

On the cardinality of semistar operations of finite character on integral domains

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Published: Sep 30, 2014
Keywords:
semistar operation of finite character, Pr\"ufer domain
Mathematics Subject Classification:
3A15, 13G05, 13F05.

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Gyu Whan Chang
Department of Mathematics, University of Incheon, Incheon 406-772, Republic of Korea

Abstract

Let D be an integral domain with Spec(D) finite, K the quotient field of D, [D,K] the set of rings between D and K, and SFc(D) the set of semistar operations of finite character on D. It is well known that |Spec(D)|≤|SFc(D)|. In this paper, we prove that |Spec(D)|=|SFc(D)| if and only if D is a valuation domain, if and only if |Spec(D)|=|[D,K]|. We also study integral domains D such that |Spec(D)|+1=|SFc(D)|.


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Supporting Agencies

This work was supported by the Incheon National University Research Fund in 2013 (Grant No. 20130395).

References

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