proofer domain

ganitat, proofer kshetra haah eka prakarcha parivartaneey ring aahe joou notherian nasalelya sandarbhat dedeckind kshetranche samanyikaran karato. yaa ringjamadhye dedeckind domenche changle aadarsh aanee module saiddhantik gunadharm aahet, parantu sahasa keval maryaditpane tayar kelelya modulesathi. german ganitshastradnya heinz proofer yanchya navavarun proofer kshetranna nave denyat aalee aahet.
udaharane.
open complexes plain formula _ 1 vareel sampoorn karyanchi ring eka proofer domain tayar karate. jaree purnank bahupadanche ring sootra _ 2 nasale taree, tarksangat gunank asalelya purnank mulyachya bahupadanchi ring hii eka proofer domain aahe. pratyek kramankachi ring hii eka dedeckind domain aahe, tarr tyanche union, bijganitiy purnankanchi ring, eka proofer domain aahe. jyapramane dedeckind domain hii sthanik patalivar eka swatantra moolyankan ring aahe, tyachpramane proofer domain hii sthanik patalivar eka moolyankan ring aahe, jenekarun proofer domain dedeckind domenche naun-notherian analogue mhanoon karya karatat. kharokhar, eka domain jeey proofer domain asalelya suburingschee thet maryada aahe teey eka proofer domain aahe.
anek proofer domain dekhil bezout domain aahet, mhanje, keval maryaditpane tayar kelelya aadarshanna prakshepak nasatat, tarr teey agadi mukt (mhanje, mukhya) asatat. udaharanarth, konatyahi compact nasalelya reeman prushthbhagavaril vishleshanatmak karyanchi ring hii baseout domain aahe aanee bijganitiy purnankanchi ring baseout aahe.
vyakhya.
proofer domain heey ardh-aanuvanshik avibhajya domain aahe. samatulya, proofer domenchi vyakhya shoonya vibhajkanshivaychi parivartaneey ring mhanoon kelee jaau shakate jyamadhye pratyek shoonya nasalela maryaditpane tayar kelela aadarsh ulat karata yeto. proofer kshetranchi anek bhinn vaishishtye dnyat aahet. borbaki tyapaiki chauda soochibaddha karate, sumare chalis aahet aanee nauu saha ughadate.
eka namuna mhanoon, avibhajya kshetravaril "r" vareel khaleel atty "r" heey eka proofer kshetra asanyaitke aahet, i.eae. r" chaa pratyek maryaditpane tayar kelela ideal prakshepak aaheh
samanyikaran.
adhik samanyatah, proofer ring hii eka parivartaneey ring aahe jyamadhye keval shunyetar vibhajkancha samavesh asalela pratyek shunyetar maryaditpane tayar kelela aadarsh ulat karata yeto (mhanje prakshepak).
jarr 'aar' madheel pratyek kamal aadarsh 'emm' sathee, 'emm' varr 'aar' chey sthanikikaran 'aar' emm 'heey sakhali ring asel tarr parivartaneey ring ankganitiy mhatale jaate. yaa vyakhyesah, ankganitiy kshetra heey eka proofer kshetra aahe.
gair-vinimayatmak ujavya kinwa davya ardh-aanuvanshik kshetranna dekhil proofer kshetranche samanyikaran manale jaau shakate.

