### Abstract

Let A be a finite dimensional associative algebra over the field F where F is a finite (algebraic) extension of the function field F_{q}(X_{1},..., X_{m}). Here F_{q} denotes the finite field of q elements (q=p^{l} for a prime p). We address the problem of computing the Jacobson radical Rad (A) of A and the problem of computing the minimal ideals of the radical-free part (Wedderburn decomposition). The algebra A is given by structure constants over F and F is given by structure constants over F_{q}(X_{1},..., X_{m}). We give algorithms to find these structural components of A. Our methods run in polynomial time if m is constant, in particular in the case m=1. The radical algorithm is deterministic. Our method for computing the Wedderburn decomposition of A uses randomization (for factoring univariate polynomials over F_{q}).

Original language | English |
---|---|

Pages (from-to) | 71-90 |

Number of pages | 20 |

Journal | Applicable Algebra in Engineering, Communication and Computing |

Volume | 5 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 1994 |

### Fingerprint

### Keywords

- Associative algebras
- symbolic computation

### ASJC Scopus subject areas

- Theoretical Computer Science
- Applied Mathematics
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

_{q}(X

_{1},..., X

_{m}).

*Applicable Algebra in Engineering, Communication and Computing*,

*5*(2), 71-90. https://doi.org/10.1007/BF01438277

**Decomposition of algebras over F _{q}(X_{1},..., X_{m}).** / Ivanyos, Gábor; Rónyai, L.; Szántó, Ágnes.

Research output: Contribution to journal › Article

_{q}(X

_{1},..., X

_{m})',

*Applicable Algebra in Engineering, Communication and Computing*, vol. 5, no. 2, pp. 71-90. https://doi.org/10.1007/BF01438277

_{q}(X

_{1},..., X

_{m}). Applicable Algebra in Engineering, Communication and Computing. 1994 Mar;5(2):71-90. https://doi.org/10.1007/BF01438277

}

TY - JOUR

T1 - Decomposition of algebras over Fq(X1,..., Xm)

AU - Ivanyos, Gábor

AU - Rónyai, L.

AU - Szántó, Ágnes

PY - 1994/3

Y1 - 1994/3

N2 - Let A be a finite dimensional associative algebra over the field F where F is a finite (algebraic) extension of the function field Fq(X1,..., Xm). Here Fq denotes the finite field of q elements (q=pl for a prime p). We address the problem of computing the Jacobson radical Rad (A) of A and the problem of computing the minimal ideals of the radical-free part (Wedderburn decomposition). The algebra A is given by structure constants over F and F is given by structure constants over Fq(X1,..., Xm). We give algorithms to find these structural components of A. Our methods run in polynomial time if m is constant, in particular in the case m=1. The radical algorithm is deterministic. Our method for computing the Wedderburn decomposition of A uses randomization (for factoring univariate polynomials over Fq).

AB - Let A be a finite dimensional associative algebra over the field F where F is a finite (algebraic) extension of the function field Fq(X1,..., Xm). Here Fq denotes the finite field of q elements (q=pl for a prime p). We address the problem of computing the Jacobson radical Rad (A) of A and the problem of computing the minimal ideals of the radical-free part (Wedderburn decomposition). The algebra A is given by structure constants over F and F is given by structure constants over Fq(X1,..., Xm). We give algorithms to find these structural components of A. Our methods run in polynomial time if m is constant, in particular in the case m=1. The radical algorithm is deterministic. Our method for computing the Wedderburn decomposition of A uses randomization (for factoring univariate polynomials over Fq).

KW - Associative algebras

KW - symbolic computation

UR - http://www.scopus.com/inward/record.url?scp=0010950716&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010950716&partnerID=8YFLogxK

U2 - 10.1007/BF01438277

DO - 10.1007/BF01438277

M3 - Article

VL - 5

SP - 71

EP - 90

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

SN - 0938-1279

IS - 2

ER -