2. EXTENSlON FlELDS
DenA Sield E tsan exenson Gfelds a field f
FE
E Ris an enenm field oj, Q
S o extension field o R d R
k h.0 neckea's maoAL)
Ler F be a idd and ut An) be a noonstas
in F[ n thaA ausk am emlens.o
freld E k F
F ond om e f s h hat f l ) =0.
have me theoaar)
e
L F afield, tman evet nontonsers ohyor
dun) F («) Cn be faco ed imo peodme oy
, isaud
i68dnesbla
nebbla pelnanl, iAnadusble polgnonals ta unane
enpt foa oRdas wd fos un (e non 3uo consroo
facwas F.
hak
Henu fen) as a fathorngatiov in F [a1 into pdgona
ONAL Saed uesble ve F.
RLduesble panonal in sneh a, facokngaton.
e PC) be an
to fnd an enen Ron idd E o, F
I-is eleasluy sovient
such ha 20
cootabnsA an elemant o pa) .
"
ne thoDRA) An Sdeal <Pea)> r io} FCaJ
<PCa)7 s
is SApd uesbla v u F [ * ) , <P(r)7
Manomal
hanomal
b )
mano ma 6ded in Fl
Aield
So F po)
subfield q /Pra)
ke deified blb
daur t h a
Se dauno
ke f cn
an
2:F F
se tha ap
In a nawal O
3ven by a e F.
+<Pem foA a e
2 (a)
fs map
ca) P6)
a
abbéF
F
7= b t <PCx2
a a t pm aN
N ) ae N
a-b e<pm)
So Ca-b) musr be a mulhp P n ) wolb deg saa zl
Na abe a-bEF
DenA Sield E tsan exenson Gfelds a field f
FE
E Ris an enenm field oj, Q
S o extension field o R d R
k h.0 neckea's maoAL)
Ler F be a idd and ut An) be a noonstas
in F[ n thaA ausk am emlens.o
freld E k F
F ond om e f s h hat f l ) =0.
have me theoaar)
e
L F afield, tman evet nontonsers ohyor
dun) F («) Cn be faco ed imo peodme oy
, isaud
i68dnesbla
nebbla pelnanl, iAnadusble polgnonals ta unane
enpt foa oRdas wd fos un (e non 3uo consroo
facwas F.
hak
Henu fen) as a fathorngatiov in F [a1 into pdgona
ONAL Saed uesble ve F.
RLduesble panonal in sneh a, facokngaton.
e PC) be an
to fnd an enen Ron idd E o, F
I-is eleasluy sovient
such ha 20
cootabnsA an elemant o pa) .
"
ne thoDRA) An Sdeal <Pea)> r io} FCaJ
<PCa)7 s
is SApd uesbla v u F [ * ) , <P(r)7
Manomal
hanomal
b )
mano ma 6ded in Fl
Aield
So F po)
subfield q /Pra)
ke deified blb
daur t h a
Se dauno
ke f cn
an
2:F F
se tha ap
In a nawal O
3ven by a e F.
+<Pem foA a e
2 (a)
fs map
ca) P6)
a
abbéF
F
7= b t <PCx2
a a t pm aN
N ) ae N
a-b e<pm)
So Ca-b) musr be a mulhp P n ) wolb deg saa zl
Na abe a-bEF
