Uppers to zero and semistar operations in polynomial rings
نویسندگان
چکیده
منابع مشابه
Uppers 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, ...
متن کاملUppers to Zero in Polynomial Rings and Prüfer-like Domains
Let D be an integral domain and X an indeterminate over D. It is well known that (a) D is quasi-Prüfer (i.e, its integral closure is a Prüfer domain) if and only if each upper to zero Q in D[X] contains a polynomial g ∈ D[X] with content cD(g) = D; (b) an upper to zero Q in D[X] is a maximal t-ideal if and only if Q contains a nonzero polynomial g ∈ D[X] with cD(g) v = D. Using these facts, the...
متن کاملNagata Rings, Kronecker Function Rings and Related Semistar Operations
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...
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 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 ine...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.06.010