J. Aust. Math. Soc.  77 (2004), 123-128
Involutions on finite-dimensional algebras over real closed fields

W. D. Munn
  Department of Mathematics
  University of Glasgow
  Glasgow G12 8QW

It is shown that the following conditions on a finite-dimensional algebra $A$ over a real closed field or an algebraically closed field of characteristic zero are equivalent: (i) $A$ admits a special involution, in the sense of Easdown and Munn, (ii) $A$ admits a proper involution, (iii) $A$ is semisimple.
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