Description of Real $AW^*$-Factors of Type I

In the paper, real $AW^*$-algebras are considered, i.e., real $C^*$-algebras which are Baer *-rings. It is proved that every real $AW^*$-factor of type I (i.e., having a minimal projection) is isometrically *-isomorphic to the algebra $B(H)$ of all bounded linear operators on a real or quaternionic Hilbert space $H$ and, in particular, is a real $W^*$-factor. In the case of complex $AW^*$-algebras, a similar result was proved by Kaplansky.