Its elements are formal sums with . In the direct sum, only finitely many components of an
element may be nonzero. No analytic convergence is required
for an element of
(Chmutov and Duzhin 2005, p. 2).
Chmutov, S. and Duzhin, S. "The Kontsevich Integral." 15 Feb 2005. https://arxiv.org/abs/math/0501040v3.Chmutov,
S. and Duzhin, S. "Kontsevich Integral." In Encyclopedia of Mathematical
Physics, Vol. 3 (Ed. J.-P. Françoise, G. L. Naber,
and S. T. Tsou). Oxford, England: Elsevier, pp. 231-239, 2006. https://doi.org/10.1016/B0-12-512666-2/00241-8.
is the direct product
with 
. In the direct sum 
, only finitely many components of an
element may be nonzero. No analytic convergence is required
for an element of 
(Chmutov and Duzhin 2005, p. 2).
is a nonnegatively graded algebra, its multiplication
extends to the graded completion by the rule
