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The purpose of this paper is to compute the number of semistar operations of certain classes of finite dimensional Pr\"ufer domains. We prove that $|SStar(R)|=|Star(R)|+|Spec(R)|+|Idem(R)|$ where $Idem(R)$ is the set of all nonzero idempotent prime ideals of $R$ if and only if $R$ is a Pr\"ufer domain with $Y$-graph spectrum, that is, $R$ is a Pr\"ufer domain with exactly two maximal ideals $M$ and $N$ and $Spec(R)=\{(0)\subsetneq P_{1}\subsetneq\dots\subsetneq P_{n-1}\subsetneq M, N\,|\, P_{n-1}\subsetneq N\}$. We also characterize non-local Pr\"ufer domains $R$ such that $|SStar(R)|=7$, respectively $|SStar(R)|=14$.
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참고문헌 (38)
참고문헌 신청
Gyu Whan Chang / 2007 / Uppers to zero and semistar operations in polynomial rings / Journal of Algebra 318(1):484~493
Gyu Whan Chang / 2013 / Polynomial extensions of semistar operations / Journal of Algebra 390:250~263
David E Dobbs / 1984 / Conducive integral domains / Journal of Algebra 86(2):494~510
Jesse Elliott / 2014 / Semistar Operations on Dedekind Domains / Communications in Algebra 43(1):236~248
Carmelo A. Finocchiaro / 2016 / Spectral spaces of semistar operations / Journal of Pure and Applied Algebra 220(8):2897~2913
Gyu Whan Chang / 2013 / Polynomial extensions of semistar operations / Journal of Algebra 390:250~263
David E Dobbs / 1984 / Conducive integral domains / Journal of Algebra 86(2):494~510
Jesse Elliott / 2014 / Semistar Operations on Dedekind Domains / Communications in Algebra 43(1):236~248
Carmelo A. Finocchiaro / 2016 / Spectral spaces of semistar operations / Journal of Pure and Applied Algebra 220(8):2897~2913
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