invertible formal power series
is invertible in the ring iff is invertible in the ring .
Proof. . Let have the multiplicative inverse . Since
we see that , i.e. is an invertible element (unit) of .
. Assume conversely that is invertible in . For making from a formal power series
This equation means that
vanishes for all ; since , the product of the formal power series (1) and (2) becomes simply equal to 1. Accordingly, is invertible.
|Title||invertible formal power series|
|Date of creation||2016-04-27 10:47:14|
|Last modified on||2016-04-27 10:47:14|
|Last modified by||pahio (2872)|