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.
Titolo: | Decomposition of Algebras |
Autori interni: | |
Anno del prodotto: | 1989 |
Rivista: | |
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. |
Handle: | http://hdl.handle.net/11568/16007 |
ISBN: | 3540510842 |
Appare nelle tipologie: | 4.1 Contributo in Atti di convegno |
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