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Von Neumann regular rings. 2nd ed. (English) Zbl 0749.16001
Malabar, Fl: Krieger Publishing Company. xvi, 412 p. (1991).
This is the second edition of the original publication (1979; Zbl 0411.16007), noted for being the first and still the most comprehensive account of regular rings. The topics covered are as in the original edition: regular rings; idempotents and projective modules; abelian regular rings; unit-regular rings; direct finiteness; rings with primitive factors artinian; bounded index of nilpotence; comparability; regular self-injective rings; structure theory for regular self-injective rings; relative dimension theory for nonsingular injective modules; infinite dimension theory for nonsingular injective modules; continuous regular rings; $\aleph\sb 0$-continuous regular rings; $K\sb 0$; pseudo- rank functions; structure of $\bbfP(R)$; existence and uniqueness of pseudo-rank functions; completions; completions with respect to families of pseudo-rank functions; completeness versus self-injectivity. There is an appendix on compact convex sets, a list of 57 open problems, and a bibliography of 270 entries. To this material is now added an overview of some of the progress made since the first edition. This consists of comments and solutions to many of the open questions, and an outline of research on the following topics: unit regularity; cancellation and stable range; bounded index; self-injectivity; ideals in regular self- injective rings; $\aleph\sb 0$-continuity; projective modules over $\aleph\sb 0$-continuous regular rings; $K\sb 0$; $K\sb 0$ for rings without unit; rank-metric completions; $N\sp*$-completions; $N\sp*$- completeness; ideal lattices, finite group actions; products of idempotents. Finally, the list of bibliography is in this way extended to 421 items.

MSC:
16-02Research monographs (associative rings and algebras)
16E50Von Neumann regular rings and generalizations
16D50Injective modules, self-injective rings (associative rings and algebras)
16S50Endomorphism rings: matrix rings