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

Gábor Ivanyos, L. Rónyai, Ágnes Szántó

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)71-90
Number of pages20
JournalApplicable Algebra in Engineering, Communication and Computing
Volume5
Issue number2
DOIs
Publication statusPublished - Mar 1994

Fingerprint

Algebra
Polynomials
Decomposition
Decompose
Computing
Free radicals
Algebraic extension
Free Radicals
Jacobson Radical
Associative Algebra
Factoring
Finite Dimensional Algebra
Function Fields
Randomisation
Univariate
Galois field
Polynomial time
Denote
Polynomial

Keywords

  • Associative algebras
  • symbolic computation

ASJC Scopus subject areas

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

Cite this

Decomposition of algebras over Fq(X1,..., Xm). / Ivanyos, Gábor; Rónyai, L.; Szántó, Ágnes.

In: Applicable Algebra in Engineering, Communication and Computing, Vol. 5, No. 2, 03.1994, p. 71-90.

Research output: Contribution to journalArticle

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