▁exist ▁a ▁unique ▁mon ic ▁polynomial ▁ ▁of ▁degree ▁ ▁and ▁a ▁unit ▁element ▁ ▁such ▁that ▁. ▁( No ether ▁normal ization ) ▁If ▁ ▁is ▁an ▁ideal , ▁then ▁there ▁is ▁a ▁finite ▁hom omorphism ▁. ▁ ▁As ▁consequence ▁of ▁the ▁division , ▁prepar ation ▁the or ems ▁and ▁No ether ▁normal ization , ▁ ▁is ▁a ▁No ether ian ▁unique ▁factor ization ▁domain ▁of ▁Kr ull ▁dimension ▁n . ▁An ▁analog ▁of ▁Hil bert ' s ▁Null stell ens atz ▁is ▁valid : ▁the ▁radical ▁of ▁an ▁ideal ▁is ▁the ▁intersection ▁of ▁all ▁maximal ▁ide als ▁containing ▁the ▁ideal . ▁ ▁Results ▁▁ ▁Results ▁for ▁polynomial ▁rings ▁such ▁as ▁H ens el ' s ▁lemma , ▁division ▁algorithms ▁( or ▁the ▁theory ▁of ▁Gro b ner ▁basis ) ▁are ▁also ▁true ▁for ▁the ▁ring ▁of ▁restricted ▁power ▁series . ▁Through out ▁the ▁section , ▁let ▁A ▁denote ▁a ▁linear ly ▁top olog ized ▁ring , ▁separated ▁and ▁complete . ▁ ▁( H ens el ) ▁Let ▁ ▁a ▁maximal ▁ideal ▁and ▁ ▁the ▁quot ient ▁map . ▁Given ▁a ▁ ▁in ▁, ▁if ▁ ▁for ▁some ▁mon ic ▁polynomial ▁ ▁and ▁a ▁restricted ▁power ▁series ▁ ▁such ▁that ▁ ▁generate ▁the ▁unit ▁ideal ▁of ▁, ▁then ▁there ▁exist ▁ ▁in ▁ ▁and ▁ ▁in ▁ ▁such ▁that ▁. ▁ ▁Notes ▁ ▁References ▁Bour b aki , ▁Alg è bre ▁commut ative ▁▁▁▁ ▁Sieg fried ▁Bos ch , ▁L ect ures ▁on ▁F ormal ▁and ▁R ig id ▁Ge ometry ,