Rational formulas for traces in zero-dimensional algebras

CARLOS D'ANDREA; GABRIELA JERONIMO

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING

Springer

Lugar: Berlin / Heidelberg; Año: 2008 vol. 19 p. 495 - 508

0938-1279

We present a rational expression for the trace of the multiplicationmap $mbox{Times}_r:A o A$ in a finite-dimensional algebra $A:=K[x_1,ldots,x_n] /mathcal{I}$ in terms of the generalized Chowform of $mathcal{I}$. Here, $mathcal{I}subsetK[x_1,ldots,x_n]$ is a zero-dimensional ideal, $K$ is a fieldof characteristic zero, and $r(x_1,dots, x_n)$ a rational functionwhose denominator is not a zero divisor in $A$.  If $mathcal{I}$ isa complete intersection in the torus, we get numerator anddenominator formulas for traces in terms of sparse resultants.