::::: E F EXT " Some - c x . PI roots of unity " - PowerPoint PPT Presentation

Jan 01, 2023 •20 likes •120 views

Applications Kummer Theory II : Theorem Proof of ' Galois Lastttme Great . Necessary feel Thu ( Kummer Theory ) ::::: E F EXT " Some - c x . PI roots of unity " already proved " the we

Applications Kummer Theory II :
Theorem Proof of ' Galois Lastttme Great . Necessary feel Thu ( Kummer Theory ) ÷÷÷:÷÷:÷÷:÷:÷÷:÷÷÷÷ E F EXT " Some - c x .
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- wmp ① F Pek rfpl that Strategy so - : mth not the primitive is where Wm 'm wi at unity and therefore - pm ) c- FIX ② show xm , - ( pm ) " m c- FIX ) - p " " " x = × field ⑦ Argue splitting k is the that e FCB ) of XII by showing K - treats are p ) - ' . . , wan { P , wnp , wip . .
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equals rm - id observe But - ' id ) - ( r - wmm - Wai id ) - w mid ) ( r ( r - id ) ( r - . ) - - - Humm ) ' ) - Nx comes them the foot - wmllx - I :( x - wm xm ( this fact and th for - id ) ( p ) all p since H - o - 13=0 , we have only fer - wmid ) Ip ) - O that fr - - ' id ) - ( r - wmm - wniid ) ( r - id ) Cr . - function . the zero " ) is a dependence array { id , r . rn poly gives . . expanding this , But → a-
that Hp ) - Wm P . there Hence 1340 - is some so XM - pm C- FIX ] . This Step ② just want we pm EF want we means . - pm for c- ( pm ) by shoving do this can We , this - Gall KIF ) all It Gall KIF ) Since Crs - . r ( pm ) - pm observe equivalent to is . - Hpk - Lumpy - pm - wi pm • 1pm ) - - - - .
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