There exist further generalizations but they do not go very far from AW*-algebras. See
http://dmle.cindoc.csic.es/pdf/PUBLICACIONSMATEMATIQUES_1995_39_01_01.pdf
There exist further generalizations but they do not go very far from AW*-algebras. See
http://dmle.cindoc.csic.es/pdf/PUBLICACIONSMATEMATIQUES_1995_39_01_01.pdf