The major algebraic aspects of von Neumann regular rings are presented in this text. The subject is developed, with detailed proofs, from the basic definitions; moreover, numerous examples
illustrating the theory are discussed. The most pervasive theme of the development is the decomposition theory of projective modules; this reflects the characteristic feature of a regular ring, namely, finitely
generated submodules of projective modules are always direct summands. Particular emphasis is placed on unit-regular rings - over these rings finitely generated projective modules can be cancelled from direct sums
- and on the Grothendieck group Ko, whose structure models the decomposition theory of finitely generated projective modules. This leads to current techniques using Ko to make the theory of partially ordered
abelian groups applicable to regular rings. |
