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Sylvester inertia law in commutative Leibniz algebras with logarithms

Przeworska-Rolewicz D.

Demonstratio Mathematica

2007

Vol. 40, nr 3

659-669

In algebras with logarithms induced by a given right invertible operator D one can define quadratic forms by means of power mappings induced by logarithmic mapping. Main results of this paper will be concerned with the case when an algebra X under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy+yDx for x, y is an element of dom D. If X is an locally m-convex algebra then these forms have the similar properties as quadratic forms in the Euclidian spaces En, including the Sylvester inertia law.