
theorem  :: Central02b:
  for R be Skew-Field, s be Element of R
  holds the carrier of center R c= the carrier of centralizer s
proof
  let R be Skew-Field, s be Element of R;
  let x be object;
  assume
A1: x in the carrier of center R;
  the carrier of center R c= the carrier of R by Th16;
  then reconsider a = x as Element of R by A1;
  a in center R by A1;
  then a*s=s*a by Th17;
  hence thesis by Th24;
end;
