Abstract
In this paper we deal with the problem of decomposing finite communtative Q-algebras as a direct product of local Q-algebras. We solve this problem by reducing it to the problem of finding a decomposition of finite algebras over finite field. We will show that it is possible to define a lifting process that allows to reconstruct the answer over the rational numbers. This lifting appears to be very efficient since it is a quadratic lifting that doesn't require stepwise inversions. It is easy to see that the Berlekamp-Hensel algorithm for the factorization of polynomials is a special case of this argument.
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© 1989 Springer-Verlag Berlin Heidelberg
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Gianni, P., Miller, V., Trager, B. (1989). Decomposition of algebras. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_29
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DOI: https://doi.org/10.1007/3-540-51084-2_29
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