Let \(\cal{A}\) be a central simple algebra over a field k and G be a commutative group with \( \left| G \right| = \deg \left( \cal{A} \right) \). It is proved that there exists a regular field extension E/k preserving indices of k-algebras such that \( {\cal{A}} \otimes _k E \) is a crossed product with the group G. Bibliography: 11 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 356, 2008, pp. 179-188.
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Tikhonov, S.V., Yanchevskii, V.I. Abelian crossed products and scalar extensions of central simple algebras. J Math Sci 156, 954–959 (2009). https://doi.org/10.1007/s10958-009-9301-x
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DOI: https://doi.org/10.1007/s10958-009-9301-x