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On the computation of overorders

    https://doi.org/10.1142/S179304212050044XCited by:3 (Source: Crossref)

    The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper, we consider the related problems of computing all minimal overorders as well as all overorders of a given order. We use techniques from algorithmic representation theory and the theory of minimal integral ring extensions to obtain efficient and practical algorithms, whose implementation is publicly available.

    AMSC: 11Y40, 11R04

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