roe nus extensions ene Omoloc n c o am evalua nen

M. Khovamv

t 4, 2020

QUACkS Conferen c

Louis-Ka draen Rl MK frlenns erfruss aq xu 200s.o Bo18

N Kitdloo Mk A d1 wmabon L Rd -wee nn bam

evalua a holag

an 2 o. 14197

n faa 2 ca R

D-1

dnk 2

Ap 9 *************************************

**************

R D-1

** ********"*****************

:2 2

*************************** Conm, alla

koloyy e-ph e.k

A Comm frl,a R A R.eR X

:2 Aa D-1 ********** AaD ,

ex)=, ett) -o

**

***

:2

. ****** oiaL ca y

X-o, M.k, ea 133

Ra D-l

HaD genena Ca

X=hX+t R 2lh,t )

.

************************************** Drr ar- Nadan,

ase ce Ak, LHFE�

Inden pra tak o n cae

ist

R- H'Ce,Z) A72( H°( S, z) R 7h, t} akya (?, 2)

U()-vathant

rl cae

is V)-umo,tA

da 2

A R -x -t)

U(0xu(t) -equivaünt (R,As) (R,A

OS, z)

Caes

eneas , E. x (R,A) R-2lE, 5.} A Rlxl/ xE, Xr E) 2 2

ECx), &C) o A->R X, Xz E, -x XK2 E, ) A() = X,l - (eX2

A7ZLs, K RCx, m.fnehlbns

ECk,)=, ¬CX)=-| X (L.- F -

-9disn al -E,r+E

D-0- s ska Jot -(X-X-E- 4E eR mA )

RA R Ivet in R R RL

-ani hande -

D

AA A ki p o

A = D-1 R[X]/(X2-EX + E Ap= A[D-] = Ro[X]/(X?- E,X + E) AsA D

X2 Beparable separable A = i oA

R ZE1, E] - D-l Rp = R[D-1]| D E-4E 2

:2 M

Aa Ala1, a2)= RaX]/((X - a1)(X - a2)) 0 AaD D-lRoD{X]/((X - aa)(X - aa))

= RaDe1 x Rapez O e2 a1-02

a:2 a1+a2= E1 a12= E2

not an integral domain A-a2 a2-a1 2 Spanab\e exftu sian

a:2 2

2

Ra Z[o1, a2 a +a2 = E1

a12 = E

RaD = Z[a1,2, (a1 - az)

a1+a2 = E1 a1a2= E

D-1

Ojqeredas

R-2[F, E.) R 2C, 2) ,,TA, E=, dz A RLx/C-E, Xr5) A RCx/(4) UK*d) R,R, R R Iaia

in A lesdori 24s o R (-) (xi2)= X-(4T4) Xt d, X*-E, X +E

las 2 Avitors X-, X-

()-(X4,)al tle(x-4)- CX-4)»lM e (*-d A 2)=(*) (K-)

-- - - -

X

More i

zA,3s zCE,6 * ***** ***********.

1

Msteaus

o-, o= (a - a1) -(-oa X=X d (oz 2) E-X, 2 ( )

A 'Sou bi modulk B for

R,A) U(2) - qmvalio.t (R, A VMU(t) -qvaat

x-EX +E (,)K~d2) Rnan a ekoi zatun

) adan do si* ?

sda os ka o do Sotny ad.- cinoiaua? 2 H(oo.) =A-8, )R k O) -A

Ss n

P) Rossla Akkct, Eqivandat anmlan kloara lo 9, aakv 2002. ooS 77

Eqwanianamloga nea uCt)xut) ,ua) does sd n) APS

Ase da- Przxe -Si ora enslog

afna le he tan d,ard d2

do buits m quvana,fa

T TautoSano, Fixi u Rnekoriali hy k komopy a Siaple

Avo:ds sxars ( Clme- Morrs on Wallan, prau) o GLle) oans CBlanet Vo

P* *eproceh

2008.0231 Avoids s ams

sesOG)xUO\ equaiant ieo No r

(X ) (X-+2) =o Om ,2

nues c.

t vensi u's tHe c2 SD

Rlies alin ,aus Sar A Lasenyn R Rag musce's muaia, t Ron h

visihi ty L's Canaial dass a x1v 1812.lo

TLe Ce

A= RX]/(X2- EX +E2)

D- Ap = AD] = Rp X]/(X2 - EX + E)

2 separable

Rp= R{D-1] D = E -4E2

D-1 R Z[E1, E]- a:2

a:2

Aa = Ala1, a2=RaX]/(X - a1)(X -a2))

a1 ta2 = E1

a1= E not an integral domain

AaD Rap X]/((X - a1)(X - a))

RaDe1 X Rape2 :2 D-1

= A22 a1-a2

1 a2-a1

:2 2

X:2

RaD cquand a f *pana,lo R= Za1,a2 D-1 Zl1, a2, (aj - a2)] 1 ta = E1

a1a2 = E

a12= E2

U)xu)- s t equvaniat

OTqe.iedes

G) Poam CRlard) eL-s kn kauun - Sdpr& Raloa -Hoqan ea p-Pubra- walrli

GL(2) pa n lnaton Rold-wnA , Spe ca N=2) & s lnmafn

pan Fe r3 a Oidms I 2 (Ni tA M)

u oennans on ra (a

St uiss ah

CaR

oecons

TAsd

tvrel

conhalockmu

Aols ou vanbo GC(2) Pas

a cas C.

at sulued cand 1 dolafacad sul suld cadanol 2

on ,2 i1,2) &1,2 oaF

ie,2} F (e)

F, (e)- F C)s Ce) symdue dztlam

- wmo no4 faas aluli

nC, umen lacs

12 F C, Fo, F a 9doalabA x(F,c), x (F2 ca),x (Fa) eenA Sunkaan n (R3

2 s

F ce-s Sin oTc) s CF,c)=9'c)+ *%() Otcc)

2

(ow do ane k) d) s (6)

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F-, sunpad,

Fc) ev F, c) G) X (x) F) Z , e Zlx,

calod

Keme 2 can F, n F smka

pr Pouen Sedes

Pr2 P Pi-P (*,, Xz) (-a)*6a)/2 Pa PCTi,7)

Por fas =FcPa P2

ingrQ F,

Rolant wa eval s n dols

S=- P PeP s -E,0 6D-o dousta

7,T2 So as undafonwol cax

enm P |2 4 PF Pp5

Cran

/ P At wat nasbe

+2-n slak spaa P

on P,, F,,F nlnm aca A R tr)p, (X)=

h r (x)=, rt)») R 7l E., fa, P,J A RCx/xE,KrE ) x-e,xe¬, (2-*)*-2%)

PaP-2p)lp-P) Faes i nen

Sen alatuns aonme

Ges G) onloy Slouss iso ke stdaS oas (eunniat?) lin

ean e do br Ge(W). ntray Not aes 'a tl eson l

Onn2 eva -Bama

Delnm F has (T TF;)y

&eno mn aon

Fx)=**yt h.o. t Com mnnwe a soiahre Coat op{ ha

siueht on pous

(e) = 2e 2+(2t ho. t

apeos n mpax oueakk naloy fluie s

usu olomoloyy

c(,C2 ) >c (,) + c (E2) +h.o.t , Conko Cobiolisms e

Flx,y)= X*ytx*Y P-2. x = Y=2 Co Anecve -fteey Cro

*-y+h o po sere, plX, y)Ft.

In seninto am eal Ouinal planope waso t genenali ud

Co l nus, á ea ip shdt2 - Sarhn. for rouw just me. o. fnmatlan (N 2)