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Associative Algebras and Computer Algebra

A. Makhlouf
Journal / Anthology

Theoretical Computer Science
Year: 1997
Volume: 187
Page range: 123-145

The aim of this work is to show how one can study varieties of associative algebras using computer algebra. The Nonstandard point of view to describe the irreducible components is well-adapted to computer algebra. it leads to algorithms which are implemented under Mathematica Software. We give a package which helps to describe the irreducible components of the n-dimensional unitary associative algebras and nilpotent algebras. We also computer under Mathematica the second cohomology group and the set of invariant scalar products over an algebra. As illustration, the procedures are applied in this paper to study the 3-dimensional associative algebras.

*Mathematics > Algebra