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Home > Mathematics and Science Textbooks > Mathematics > Algebra > Rings Close to Regular: (545 Mathematics and Its Applications)
Rings Close to Regular: (545 Mathematics and Its Applications)

Rings Close to Regular: (545 Mathematics and Its Applications)


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About the Book

This monograph discusses rings closed to von Neumann regular rings. The following classes are considered: exchange rings, p-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 p-regular ring (a ring A is p-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 p-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.

Table of Contents:
1 Some Basic Facts of Ring Theory.- 2 Regular and Strongly Regular Rings.- 3 Rings of Bounded Index and I0-rings.- 4 Semiregular and Weakly Regular Rings.- 5 Max Rings and ?-regular Rings.- 6 Exchange Rings and Modules.- 7 Separative Exchange Rings.

About the Author :
Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.

Review :
From the reviews: "This is the first monograph on rings close to von Neumann regular rings. ... The book will appeal to readers from beginners to researchers and specialists in algebra; it concludes with an extensive bibliography." (Xue Weimin, Zentralblatt MATH, Vol. 1120 (22), 2007)


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Product Details
  • ISBN-13: 9781402008511
  • Publisher: Kluwer Academic Publishers
  • Publisher Imprint: Kluwer Academic Publishers
  • Height: 234 mm
  • No of Pages: 350
  • Returnable: Y
  • Width: 156 mm
  • ISBN-10: 1402008511
  • Publisher Date: 30 Sep 2002
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 545 Mathematics and Its Applications


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