In this paper we deal with the problem of decomposing finite commutative 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 a finite field. We show that it is possible to define a lifting process that allows one to reconstruct the answer over the rational numbers. This lifting appears to be very efficient since it is a quadratic lifting that does not 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.
Decomposition of Algebras
GIANNI, PATRIZIA;
1989-01-01
Abstract
In this paper we deal with the problem of decomposing finite commutative 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 a finite field. We show that it is possible to define a lifting process that allows one to reconstruct the answer over the rational numbers. This lifting appears to be very efficient since it is a quadratic lifting that does not 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.File in questo prodotto:
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