- For any
, we have
- If
satisfies
for some positive integer
, then
we have
- Let
be a positive integer.
If
satisfies
such thatsuch that

Recall that the ring of -adic Witt vectors is a quotient of the ring of universal Witt vectors. We have therefore a projection . But in the following we intentionally omit to write .

- Every element of
is written uniquely as
- For any
, we have
- A map
- .
- An element is invertible in if and only if is invertible in .

(i.e. $x$:invertible)

Since any integral domain can be embedded into a perfect field, we deduce the following

ARRAY(0x35e8850)ARRAY(0x35e8850)