Rational Formulas for Traces in zero-dimensional Algebras

Details Rational Formulas for Traces in zero-dimensional Algebras Rational Formulas for Traces in zero-dimensional Algebras

2005-03-30

arxiv.org/abs/math/0503721v2

Mathematics

Commutative Algebra

11 pages, latex document, revised version accepted for publication in the AAECC Journal

Scientific paper

We present a rational expression for the trace of the multiplication map M_r in a finite-dimensional algebra of the form A:=K[x_1,...,x_n]/I in terms of the generalized Chow form of I. Here, I is a zero-dimensional ideal of K[x_1,...,x_n] is a zero-dimensional ideal, K is a field of characteristic zero, and r(x_1,..., x_n) a rational function whose denominator is not a zero divisor in A. If I is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants.

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