Re: Noetherian rings

Denote J to be the ideal that is not generated by finitely many
elements. (the I's confuse me).
Let J1 be the ideal generated by x1, an element different from zero
that you picked from J. Clearly, J1\subset J.
If we cannot find an element in J outside J1, we would have J=J1,
contradicting the fact that J is not f.g.
go on!
you'll find a strictly ascending chain of ideals. The union equals J.
does this help you?

.

Relevant Pages

  • 90 Nissan Maxima No cruise control
    ... The cruise conrtol has stopped working. ... ideals on what to check? ... Jim ... Prev by Date: ...
    (rec.autos.tech)
  • Overflow?
    ... when I run an append query. ... Any ideals as to what is causing this? ... Prev by Date: ...
    (microsoft.public.access.formscoding)
  • Re: Boston Globe on J Hatto
    ... Wayne Reimer succeeds in living up to his own asseverated ... ideals. ... Prev by Date: ...
    (rec.music.classical.recordings)
  • Re: Christian Astronomers NG?
    ... If only everyone, of whatever faith or creed, practised your ideals ... this planet would have a lot less strife. ... Prev by Date: ...
    (sci.astro.amateur)
  • Re: sept 24
    ... I used a bunch of your ideals on Rainbow Survival... ... (Mother Rainbow's Group) ... Prev by Date: ...
    (alt.gathering.rainbow)