 Power-series presentation of an adic completion

ID: power-series-presentation-of-an-adic-completion

I = (a_{1}, \dots, a_{s})

X_{i} \mapsto a_{i}

gives a ring map to the

I

-adic completion, with each series evaluated modulo

I^{r}

using only terms of total degree below

r

. It is surjective: successively represent the residual class in

I^{r} / I^{r + 1}

by a homogeneous degree-

r

a_{i}

. If

R

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