Decomposition of Algebras

@inproceedings{Gianni1988DecompositionOA,
  title={Decomposition of Algebras},
  author={P. Gianni and V. Miller and Barry M. Trager},
  booktitle={ISSAC},
  year={1988}
}
  • P. Gianni, V. Miller, Barry M. Trager
  • Published in ISSAC 1988
  • Computer Science
  • 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… CONTINUE READING
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    References

    SHOWING 1-10 OF 24 REFERENCES
    Simple algebras are difficult
    • L. Rónyai
    • Mathematics, Computer Science
    • STOC '87
    • 1987
    • 35
    Zero Divisors in Quaternion Algebras
    • L. Rónyai
    • Mathematics, Computer Science
    • J. Algorithms
    • 1988
    • 22
    A remark on a paper by Wang: another surprising property of 42
    • 3
    • PDF
    Factoring polynomials with rational coefficients
    • 3,740
    • PDF
    Probabilistic Algorithms in Finite Fields
    • 330
    • PDF
    Factoring polynomials over finite fields
    • 226
    A remark on the Hensel factorization method
    • 24
    • PDF
    Factoring Polynomials Over Algebraic Number Fields
    • S. Landau
    • Mathematics, Computer Science
    • SIAM J. Comput.
    • 1985
    • 75
    On Polynomial Factorization
    • D. Lazard
    • Mathematics, Computer Science
    • EUROCAM
    • 1982
    • 10