This is the first monograph on rings closed to von Neumann regular
rings. The following classes of rings are considered: exchange
rings, pi-regular rings, weakly regular rings, rings with
comparability, V-rings, and max rings. Every Artinian or von
Neumann regular ring A is an exchange ring (this means that for
every one of its elements a, there exists an idempotent e of A such
that aA contains eA and (1-a)A contains (1-e)A). Exchange rings are
very useful in the study of direct decompositions of modules, and
have many applications to theory of Banach algebras, ring theory,
and K-theory. In particular, exchange rings and rings with
comparability provide a key to a number of outstanding cancellation
problems for finitely generated projective modules. Every von
Neumann regular ring is a weakly regular pi-regular ring (a ring A
is pi-regular if for every one of its elements a, there is a
positive integer n such that a is contained in aAa) and every
Artinian ring is a pi-regular max ring (a ring is a max ring if
every one of its nonzero modules has a maximal submodule). Thus
many results on finite-dimensional algebras and regular rings are
extended to essentially larger classes of rings. Starting from a
basic understanding of ring theory, the theory of rings close to
regular is presented and accompanied with complete proofs.
The book will appeal to readers from beginners to researchers
and specialists in algebra; it concludes with an extensive
bibliography.
General
Imprint: |
Springer-Verlag New York
|
Country of origin: |
United States |
Series: |
Mathematics and Its Applications, 545 |
Release date: |
September 2002 |
First published: |
2002 |
Authors: |
A. a. Tuganbaev
|
Dimensions: |
234 x 156 x 20mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
350 |
Edition: |
2002 ed. |
ISBN-13: |
978-1-4020-0851-1 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
General
|
LSN: |
1-4020-0851-1 |
Barcode: |
9781402008511 |
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