Splitting full matrix algebras over algebraic number fields

JOURNAL OF ALGEBRA

卷:354

Article

Ivanyos, Gabor¹  Ronyai, Lajos^1,2  Schicho, Josef³ 

[1] Hungarian Acad Sci, Comp & Automat Res Inst, H-1111 Budapest, Hungary

[2] Budapest Univ Technol & Econ, Dept Algebra, H-1111 Budapest, Hungary

[3] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, A-4040 Linz, Austria

关键词: Central simple algebra;    Splitting;    Splitting element;    Minkowski's theorem on convex bodies;    Maximal order;    Real and complex embedding;    Lattice basis reduction;    Parametrization;    Severi-Brauer surfaces;    n-Descent on elliptic curves;   

DOI  :  10.1016/j.jalgebra.2012.01.008

来源: Elsevier

【 摘 要 】

Let K be a fixed algebraic number field and let A be an associative algebra over K given by structure constants such that A congruent to M-n(K) holds for some positive integer n. Suppose that n is bounded. Then an isomorphism A -> M-n(K) can be constructed by a polynomial time ff-algorithm. An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields. As a consequence, we obtain a polynomial time ff-algorithm to compute isomorphisms of central simple algebras of bounded degree over K. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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