منابع مشابه
Finitely Ramified Iterated Extensions
Let p be a prime number, K a number field, and S a finite set of places of K. Let KS be the compositum of all extensions of K (in a fixed algebraic closure K) which are unramified outside S, and put GK,S = Gal(KS/K) for its Galois group. These arithmetic fundamental groups play a very important role in number theory. Algebraic geometry provides the most fruitful known source of information conc...
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Motivated by the construction of new examples of Artin-Schelter regular algebras of global dimension four, J.J.Zhang and J.Zhang (2008) introduced an algebra extension AP [y1, y2;σ, δ, τ ] of A, which they called a double Ore extension. This construction seems to be similar to that of a two-step iterated Ore extension over A. The aim of this paper is to describe those double Ore extensions whic...
متن کاملIterated Extensions in Module Categories
Let k be an algebraically closed field, let R be an associative kalgebra, and let F = {Mα : α ∈ I} be a family of orthogonal points in Mod(R) such that EndR(Mα) ∼= k for all α ∈ I. Then Mod(F), the minimal full subcategory of Mod(R) which contains F and is closed under extensions, is a full exact Abelian sub-category of Mod(R) and a length category in the sense of Gabriel [8]. In this paper, we...
متن کاملThe Picard–vessiot Antiderivative Closure
F is a differential field of characteristic zero with algebraically closed field of constants C. A Picard–Vessiot antiderivative closure of F is a differential field extension E ⊃ F which is a union of Picard–Vessiot extensions of F , each obtained by iterated adjunction of antiderivatives, and such that every such Picard– Vessiot extension of F has an isomorphic copy in E. The group G of diffe...
متن کاملExtensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms
Let F be a characteristic zero differential field with an algebraically closed field of constants C, E ⊃ F be a no new constant extension by antiderivatives of F and let y1, · · · yn be antiderivatives of E. The antiderivatives y1, · · · , yn of E are called J-I-E antiderivatives if y′i ∈ E satisfies certain conditions. We will discuss a new proof for the KolchinOstrowski theorem and generalize...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.03.030