ii
play

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

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 .

  3. 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 ,

  4. 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 ) -

  5. 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)=# .

  6. 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

  7. 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

  8. 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 - ,

  9. 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

  10. 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

  11. 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 - - .

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend


More recommend