Von Neumann algebras | Ring theory

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. In the literature, left Rickart rings have also been termed left PP-rings. ("Principal implies projective": See definitions below.) (Wikipedia).

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Related pages

Projective module | Injective module | Hilbert space | Abstract algebra | Complete lattice | Functional analysis | Von Neumann regular ring | Hereditary ring | Annihilator (ring theory) | Domain (ring theory) | Opposite ring | Self-adjoint | Baer *-semigroup | Von Neumann algebra | C*-algebra | Lattice (order) | AW*-algebra