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ON THE CARDINALITY OF SEMISTAR OPERATIONS OF FINITE CHARACTER ON INTEGRAL DOMAINS

  • Chang, Gyu Whan (Department of Mathematics Education Incheon National University)
  • Received : 2014.03.12
  • Accepted : 2014.09.15
  • Published : 2014.09.30

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)| ${\leq}$ |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)|.

Acknowledgement

Supported by : Incheon National University

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