Hey,

Let F be any field and let I = F[[x]] \ F[[x]]* be the set of non-units in F[[x]].

Show that I is an ideal of F[[x]].

this question is troubling me as i cannot seem to properly define what I is, can someone please explain I to me?

Cheers

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- Aug 14th 2010, 10:12 PMi_never_noticedSet of non-units in F[[x]]
Hey,

Let F be any field and let I = F[[x]] \ F[[x]]* be the set of non-units in F[[x]].

Show that I is an ideal of F[[x]].

this question is troubling me as i cannot seem to properly define what I is, can someone please explain I to me?

Cheers - Aug 15th 2010, 11:11 AMNonCommAlg
easy to prove: $\displaystyle I=\{\sum_{n=0}^{\infty} a_nx^n \in F[[x]]: \ a_0=0\}= \langle x \rangle.$ in fact $\displaystyle I$ is the unique maximal ideal of $\displaystyle F[[x]]$ because $\displaystyle F[[x]]/I \cong F,$ which is a field.