/sci/ - Science & Math

>>9985442
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How does this proof make any sense? How does he get that since [math]z[/math] is not a unit, then [math]z=z_1t[/math]?

I would have used the fact that R being Noetherian is equivalent to "any family of ideals has a maximal element", and used the "family of proper ideals" as the family in question and they hence are all contained in the unique maximal ideal since R is local. Since it is principal, then it must divide any non-unit element.