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II : " , an ) for algebraic lemme If - Fla , E - element - PowerPoint PPT Presentation

Mar 23, 2023 •149 likes •278 views

The Galois Group worked example A II : " , an ) for algebraic lemme If - Fla , E - element regal CEH ) then elements an 4 , . . , an . , . action its a , . . , an determined on by . is . . . , Olan ) , knew the values Ha

  1. The Galois Group worked example A II :

  2. " , an ) for algebraic lemme If - Fla , E - element regal CEH ) then elements an 4 , . . , an . , . action its a , . . , an determined on by . is . . . , Olan ) , knew the values Ha , ) , if Ie , . we acts EEE how t know any on Then . we is given by for ③ { me E - basis key F An : oeeiadlirf-ca.ai.im ) ) . . - men .

  4. x ' splitting field fer - LEAD be the EI let E . roots recalled are time we last = WZ 352 = w UI = 352 23 L , Lz , , - -t=w - HEI EE w ' and where - w = , az ) homework 6 On E - K . saw we ,

  5. Gal LE la ) ? what question Big is : Theoretic description ① Two answers group : more explicitly lied ② to elements of description as Anaheim Tt Gal ( E IQ ) -

  6. whiten Rachel roots told us 3 has - 2 x3 Since , E 53 Gal LE la ) that homework know Additionally 6 from you E last him since From ④ 3=6 [ E : , . we get a splitting field - QT l Gall Ela H - LE is - ' F) = 6 ⇒ LGullElQ)=# .

  7. how we understand re Gul ( El Q ) act as functions ? Can - f¥¥÷:÷÷÷÷ : : " " " iii. iii. . - - = x' tax ta ? irreaka ) Also is It , q ) → K - basis to E Q

  8. how we understand re Gul ( El Q ) act as functions ? Can - showed I :* : Rebecca h as la , da ) " " " E - that if want to - we kilo , :O . i : Q ftp.2.qa.a.az : E → E l we can - basis for T E is , up to " climbing E " K via

  9. E is tha , airman , dial Qi - basis for up to k by sending can first extend idea we . root of idairro.cat/--x3-2 to d. any 4¥ 4743 or 2 , t L , or 4 1-72 , , sending by 4 extend can then We ) of Ylirrk la ) ? xta ? not - x' ta La to - any O - - he , [ - and , so Roots at this 4k . ) as are a For example , if ' . either then flirt , aka ) ) or 221-223 - x' thx tht dats d - ,

  10. determined by rca ) =L re Gal ( Etta ) For how does r act o (a) = Lz and on , EEE ? genial a in th has expression unique A given EEE a - q , I tqratqga-tqyhatqsa.az term e - + qua ? K . r ( e ) ? what S . is

  11. 4) of g. Itza , tqga-tqyxatq.a.az So e - - + gain ) = q , tqzrkiltqgok.Ytqyokdtqs.tk . )rKr ) ' rca ) + 26 ok . ) = qtqztztqztzhtqydzt Esau , +962543 . longer in terms of " " basis Note : this our is no

  12. Onelustbkuhin , at Gul CEIHQ ) using the viewed by we field Okla ) . intermediate K - - wuthin intermediate field could One any use problem for homework : Upcoming El . through " " working by ideas then can fellow ( w ) L - - .

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