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PDF-LetRbeanorderedring.AllsquaresofnonzeroelementsofRarepositive,Rhaschar PDF document

Theorem253 ProofLetPbethepositivesetcorrespondingtotheorderingonRIfa2Rnf0gtheneitheraoraisinPandsobyclosurea2a2isalsoinPthusallsquarearepositiveUsingthis112isalwayspositivesoagainbyclo

Theorem25.3 Proof.LetPbethepositivesetcorrespondingtotheorderingonR.Ifa2Rnf0g theneitheraoraisinP andsobyclosure a2=(a)2isalsoinP;thusallsquarearepositive.Usingthis 1=12isalwayspositive soagainbyclo

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LetRbeanorderedring.AllsquaresofnonzeroelementsofRarepositive,Rhaschar: Transcript

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