On polynomial ascent and descent semistar operations on an integral domain
نویسندگان
چکیده
منابع مشابه
The semistar operations on certain Prüfer domain, II
Let D be a 1-dimensional Prüfer domain with exactly two maximal ideals. We completely determine the star operations and the semistar operations on D. Let G be a torsion-free abelian additive group. If G is not discrete, G is called indiscrete. If every non-empty subset S of G which is bounded below has its infimum inf(S) in G, then G is called complete. If G is not complete, G is called incompl...
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Given a stable semistar operation of finite type ⋆ on an integral domain D, we show that it is possible to define in a canonical way a stable semistar operation of finite type [⋆] on the polynomial ring D[X], such that D is a ⋆-quasi-Prüfer domain if and only if each upper to zero in D[X] is a quasi-[⋆]-maximal ideal. This result completes the investigation initiated by Houston-Malik-Mott [18, ...
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If D is an integral domain with quotient field K, then let F̄(D) be the set of non-zero D-submodules of K, F(D) be the set of non-zero fractional ideals of D and f(D) be the set of non-zero finitely generated D-submodules of K. A semistar operation ? on D is called arithmetisch brauchbar (or a.b.) if, for every H ∈ f(D) and every H1, H2 ∈ F̄(D), (HH1) ? = (HH2) ? implies H 1 = H ? 2 , and ? is ca...
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ژورنال
عنوان ژورنال: Mathematical Journal of Ibaraki University
سال: 2010
ISSN: 1883-4353,1343-3636
DOI: 10.5036/mjiu.42.3