Splitting Fields and Separability
نویسندگان
چکیده
منابع مشابه
Splitting Families and Complete Separability
The purpose of this short note is to answer a question posed by the second and third authors in [5] and to use this to solve a problem of Shelah [6]. We say that two infinite subsets a and b of ω are almost disjoint or a.d. if a∩ b is finite. We say that a family A of infinite subsets of ω is almost disjoint or a.d. if its members are pairwise almost disjoint. A Maximal Almost Disjoint family, ...
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In this paper, we study separability of graded field extensions. In particular, without restriction to torsion free of the grade group, we show that some separability results of graded field extensions given in [7] hold. On the other hand, the separability notions defined in [1] do not cover many situations, for example group algebras. We show that these notions are simple cases of separability...
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In the noncommutative case also a version of (1) can be proved; see for instance [S, Proposition A.33. In that case, in general, such an N is not finitely generated over K. What (2) means for the noncommutative case depends on how one defines the phrase “constructing by repeatedly adding zeros of p until p has a complete set of zeros.” The adding of zeros may be done by forming field coproducts...
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We show that every algebraic group of type E8 over any field becomes split over some field extension of degree dividing 26 · 32 · 5 = 2880. This improves a bound by Tits and, in fact, is optimal.
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We provide some algorithms for dynamically obtaining both a possible representation of the splitting field and the Galois group of a given separable polynomial from its universal decomposition algebra. c © 2006 Elsevier Ltd. All rights reserved.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.2307/2038936