Regular representations of finite-dimensional separable semisimple algebras and Grobner bases
Let A be a semisimple n-dimensional commutative algebra over a field IF. It is easy to see that, given a basis B of A, the transposes of the matrices over F that represent a is an element of A regularly with respect to B can be simultaneously diagonalized over many fields. Using the multiplication table of the algebra we construct an ideal I of F[x(1),..., x(n)] given in terms of a Grobner basis of the ideal I with respect to a total degree lexicographic monomial ordering and show that A is isomorphic to F[x(1),..., x(n)]/I. We will then use Grobner basis properties to prove the properties of the algebra. (C) 2003 Elsevier Ltd. All rights reserved.
regular representation semisimple algebras grobner bases