Integrally Closed Domains with Only Finitely Many Star Operations |
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Authors: | Evan Houston Abdeslam Mimouni |
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Institution: | 1. Department of Mathematics and Statistics , University of North Carolina at Charlotte , Charlotte , North Carolina , U.S.A.;2. Department of Mathematics and Statistics , King Fahd University of Petroleum &3. Minerals , Dhahran , Saudi Arabia |
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Abstract: | We prove that an integrally closed domain R admits only finitely many star operations if and only if R satisfies each of the following conditions: (1) R is a Prüfer domain with finite character, (2) all but finitely many maximal ideals of R are divisorial, (3) only finitely many maximal ideals of R contain a nonzero prime ideal that is contained in some other maximal ideal of R, and (4) if P ≠ (0) is the largest prime ideal contained in a (necessarily finite) collection of maximal ideals of R, then the prime spectrum of R/P is finite. |
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Keywords: | Conducive domain Prüfer domain Star operation |
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