منابع مشابه
Local–global Properties for Semistar Operations
We study the “local” behavior of several relevant properties concerning semistar operations, like finite type, stable, spectral, e.a.b. and a.b. We deal with the “global” problem of building a new semistar operation on a given integral domain, by “gluing” a given homogeneous family of semistar operations defined on a set of localizations. We apply these results for studying the local–global beh...
متن کاملA Note on the Cancellation Properties of Semistar Operations
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...
متن کاملThe 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...
متن کاملSemistar dimension of polynomial rings and Prufer-like domains
Let $D$ be an integral domain and $star$ a semistar operation stable and of finite type on it. We define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong S-domains. As an application, we give new characterizations of $star$-quasi-Pr"{u}fer domains and UM$t$ domains in terms of dimension inequal...
متن کاملUppers to Zero and Semistar Operations in Polynomial Rings
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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ژورنال
عنوان ژورنال: Mathematical journal of Ibaraki University
سال: 2003
ISSN: 1883-4353,1343-3636
DOI: 10.5036/mjiu.35.11