Injectivity and nuclearity properties for real C*-algebras

In this paper, we study injective and nuclear real W$^*$- and C$^*$-algebras. The connection of these concepts with similar concepts of enveloping W$^*$- and C$^*$-algebras is considered. The equivalence of the concepts of injectivity and nuclearity for real C$^*$-algebras is shown. As a consequence, nuclear real factors of types II$_1,$ II$_\infty,$ III$_1,$ III$_0,$ and III$_\lambda$ ($0<\lambda<1$) are completely described.