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Integral domains with finitely many spectral semistar operations

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Abstract

Let D be a finite-dimensional integral domain, Spec(D) be the set of prime ideals of D, and SpSS(D) be the set of spectral semistar operations on D. Mimouni gave a complete description for the prime ideal structure of D with SpSS(D) = n + dim(D) for 1 ≤ n ≤ 5 except for the quasi-local cases of n = 4, 5. In this paper, we show that there is an integral domain D such that SpSS(D) = n+dim(D) for all positive integers n with n ≠ 2. As corollaries, we completely characterize the quasi-local domains D with SpSS(D) = n+dim(D) for n = 4, 5. Furthermore, we also present the lower and upper bounds of SpSS(D) when Spec(D) is a finite tree.

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Authors and Affiliations

  1. Department of Mathematics Education, Incheon National University, Incheon, 22012, Republic of Korea

    Gyu Whan Chang

  2. Department of Mathematics Education, Chosun University, Gwangju, 61452, Republic of Korea

    Dong Yeol Oh

Authors
  1. Gyu Whan Chang
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  2. Dong Yeol Oh
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Correspondence to Dong Yeol Oh.

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Chang, G.W., Oh, D.Y. Integral domains with finitely many spectral semistar operations. Front. Math. China 12, 35–49 (2017). https://doi.org/10.1007/s11464-016-0587-y

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  • DOI: https://doi.org/10.1007/s11464-016-0587-y

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