On semifinite AW*-algebras
J. D. Maitland Wright · Mathematical Proceedings of the Cambridge Philosophical Society · 1976
Kaplansky (8, 9, 10) introduced the concept of an AW*-algebra and, by purely algebraic methods, succeeded in extending the ‘Type Theory’ of Murray and von Neumann from W*-algebras to these more general algebras. Every W*-algebra is an AW*-algebra but the converse is false, for there exist commutative AW*-algebras which are not W*-algebras.