PRÜFER ⋆-MULTIPLICATION DOMAINS AND SEMISTAR OPERATIONS
نویسندگان
چکیده
منابع مشابه
A "υ-Operation Free" Approach to Prüfer υ-Multiplication Domains
The so-called Prüfer υ-multiplication domains PυMDs are usually defined as domains whose finitely generated nonzero ideals are t-invertible. These domains generalize Prüfer domains and Krull domains. The PυMDs are relatively obscure compared to their verywell-known special cases. One of the reasons could be that the study of PυMDs uses the jargon of star operations, such as the υ-operation and ...
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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...
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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...
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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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In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer’s book [20]) and, hence, the related classical theory of ideal systems based on the works by W. Krull, E. Noether, H. Prüfer and P. Lorenzen from 1930’s. In [17] and [18] the current authors investigated properties of the Kronecker functi...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2003
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498803000349