maximal ideals of ring of formal power series
Also the converse is true, i.e. if is a maximal ideal of , then there is a maximal ideal
of such that .
Note. In the special case that is a field, the only maximal ideal of which is the zero ideal , this corresponds to the only maximal ideal of (see http://planetmath.org/node/12087formal power series over field).
We here prove the first assertion. So, is assumed to be maximal. Let
be any formal power series in . Hence, the constant term cannot lie in . According to the criterion for maximal ideal, there is an element of such that . Therefore
whence the same criterion says that is a maximal ideal of .
|Title||maximal ideals of ring of formal power series|
|Date of creation||2013-03-22 19:10:49|
|Last modified on||2013-03-22 19:10:49|
|Last modified by||pahio (2872)|