ExTEN S1ON THeoR t
A fie tsormoR PHLM Prce hi ideshty
Sd rmoapi
somo eph
í3r entensio n eozer,
e isomopnism t
o an
enended
be
F Com
naed le
Somoxpso Fatensson 1heou ovoo
ha r uaves
a ves f imed
1le
Fha r
a *eld F. Le subfield
er E be an algebkaie eakns5on oph a
be o F enbo a eld F '. Let E' be
F'be Shes a r
Cwn moaph a on enrenSen
e n
haokaM e oap
C a n be enkndrd bo an bomorphisro
F.
algebaauu elosRL F . un LA b emto a safield o
F
isopapsv t e E a suafeld Fsuuh o enkndad to an
Isomoapum
ernbe have tË) : F'
F e mus
a) cla) for al ae F. E
TE
Cocolo Than F. Let be an
enenson 4E umd eE L
Ebe a inse enension a ficld
bEF i algebai e o
Fbe an algebuaic
om
lo a field F. and lat
hon ísomorpmis e F
ev F, then the to S0 norpnís w
Cogae emnnons o o lo An
emended o
om isonoRphism
elosun P. hen the numba k
FCB), aAD be an
aM.F(«) >
m o phisro c t E subfield
a F'i Siite i
F
ento a subfitld o ar t e nurobea »
Sndapendsov o F, F' avnd .
nd
wo ields E
erenssns toroplateg daseami ned b m
Paee -PR) s u hotnsie to tne
She potf i boredbo o Somorphv enension Husu)
eAoplaLt F Fl),Fb Fp)and Fy f
TtCat)G),
et ond
etwo algebrauic closunes F . un
P i s phht to f undu
Gach isomoapns) Leavig an
F
euno o F med F
, 1pmophusms ond ( au)
onsd o
on
wpeth
Now i an
clos wesh and e coRaDopondonto behween f
show Ha,
ome o o
u ome one On view og
omenson eoaom and s 2" Coaolony ardla 2 : E> f
Jn
b uooRhg L s iodaperior
enrendsg he no:o o 5 enerdg
: F Co KR
ndince
an
s tso morhism F finsre foll os
s f i n i e foll
*neod
ppo
hnsre enhenson ok
m noo
ie
CoMperds to eAth
TiE Ethor ee nds O ron ha aey thor Sh is
e coan on somoaphism fa (erotnsb ) )duy 5om
E F(di do fir h
en caneod ores
a £ and A th bo.og pocsbl
b Slaui gonq
l aAL mu a fins
bun to h2 Rme- Cii) in F fon 5
l ) : (Au)C)¥ACE aim
JHen algebraicaluuy, T 9ARC F) Ao +;2
hu
T(a) musr e on
EF un
wh aik
(t*))
2esos
(aio) la)a*
)")
)
Pe onna
TrasCL rs 2 afield F. Te ne
Oe e. ishe ênesv
sad w C2 ket E a
1hfar ha we tousd ve
uovusd saahng ar E ad gou ti* to
H . nde E : Ft E vex F
WHen elsaboteUy, Tla): (x'tl«)
A fie tsormoR PHLM Prce hi ideshty
Sd rmoapi
somo eph
í3r entensio n eozer,
e isomopnism t
o an
enended
be
F Com
naed le
Somoxpso Fatensson 1heou ovoo
ha r uaves
a ves f imed
1le
Fha r
a *eld F. Le subfield
er E be an algebkaie eakns5on oph a
be o F enbo a eld F '. Let E' be
F'be Shes a r
Cwn moaph a on enrenSen
e n
haokaM e oap
C a n be enkndrd bo an bomorphisro
F.
algebaauu elosRL F . un LA b emto a safield o
F
isopapsv t e E a suafeld Fsuuh o enkndad to an
Isomoapum
ernbe have tË) : F'
F e mus
a) cla) for al ae F. E
TE
Cocolo Than F. Let be an
enenson 4E umd eE L
Ebe a inse enension a ficld
bEF i algebai e o
Fbe an algebuaic
om
lo a field F. and lat
hon ísomorpmis e F
ev F, then the to S0 norpnís w
Cogae emnnons o o lo An
emended o
om isonoRphism
elosun P. hen the numba k
FCB), aAD be an
aM.F(«) >
m o phisro c t E subfield
a F'i Siite i
F
ento a subfitld o ar t e nurobea »
Sndapendsov o F, F' avnd .
nd
wo ields E
erenssns toroplateg daseami ned b m
Paee -PR) s u hotnsie to tne
She potf i boredbo o Somorphv enension Husu)
eAoplaLt F Fl),Fb Fp)and Fy f
TtCat)G),
et ond
etwo algebrauic closunes F . un
P i s phht to f undu
Gach isomoapns) Leavig an
F
euno o F med F
, 1pmophusms ond ( au)
onsd o
on
wpeth
Now i an
clos wesh and e coRaDopondonto behween f
show Ha,
ome o o
u ome one On view og
omenson eoaom and s 2" Coaolony ardla 2 : E> f
Jn
b uooRhg L s iodaperior
enrendsg he no:o o 5 enerdg
: F Co KR
ndince
an
s tso morhism F finsre foll os
s f i n i e foll
*neod
ppo
hnsre enhenson ok
m noo
ie
CoMperds to eAth
TiE Ethor ee nds O ron ha aey thor Sh is
e coan on somoaphism fa (erotnsb ) )duy 5om
E F(di do fir h
en caneod ores
a £ and A th bo.og pocsbl
b Slaui gonq
l aAL mu a fins
bun to h2 Rme- Cii) in F fon 5
l ) : (Au)C)¥ACE aim
JHen algebraicaluuy, T 9ARC F) Ao +;2
hu
T(a) musr e on
EF un
wh aik
(t*))
2esos
(aio) la)a*
)")
)
Pe onna
TrasCL rs 2 afield F. Te ne
Oe e. ishe ênesv
sad w C2 ket E a
1hfar ha we tousd ve
uovusd saahng ar E ad gou ti* to
H . nde E : Ft E vex F
WHen elsaboteUy, Tla): (x'tl«)
