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EnglishIn 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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