Baer ring
In abstract algebra and functional analysis, Baer rings, Baer *-rings, Rickart rings, Rickart *-rings, and AW*-algebras are various attempts to give an algebraic analogue of von Neumann algebras, using axioms about annihilators of various sets. Any von Neumann algebra is a Baer *-ring, and much of the theory of projections in von Neumann algebras can be extended to all Baer *-rings, For example, Baer *-rings can be divided into types I, II, and III in the same way as von Neumann algebras.