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small things
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metakunt committed Jan 11, 2025
1 parent 2865cd4 commit fc000a0
Showing 1 changed file with 4 additions and 5 deletions.
9 changes: 4 additions & 5 deletions set.mm
Original file line number Diff line number Diff line change
Expand Up @@ -649896,16 +649896,15 @@ fixed reference functional determined by this vector (corresponding to
$)


$c AlgClosure $. $( Algebraic closure $)
$c AlgCl $. $( Algebraic closure $)

$( Integral elements of a ring. $)
calgclosure $a class AlgClosure $.
calgcl $a class AlgCl $.

${
$d k l p z f q x $.
$( Define the algebraic closure of any field. (Contributed by metakunt,
11-Jan-2025.) $)
df-algclosure $a |- AlgClosure = ( k e. Field |-> { l e. Field |
df-algcl $a |- AlgCl = ( k e. Field |-> { l e. Field |
( A. p e. ( Base ` ( Poly1 ` l ) ) ( ( deg1 ` p ) e. NN ->
E. z e. ( Base ` l ) ( ( ( eval1 ` l ) ` p ) ` z ) = ( 0g ` l ) ) /\
E. f e. ( k RingHom l ) A. x e. l E. q e. ( Base ` ( Poly1 ` k ) )
Expand All @@ -649916,7 +649915,7 @@ fixed reference functional determined by this vector (corresponding to
${
$( The algebraic closure exists for any field. We are sadly nowhere near
of proving that yet. (Contributed by metakunt, 11-Jan-2025.) $)
ax-algclex $a |- ( K e. Field -> ( AlgClosure ` K ) =/= (/) ) $.
ax-algclex $a |- ( K e. Field -> ( AlgCl ` K ) =/= (/) ) $.
$}

$(
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