Read Rings Close to Regular (Mathematics and Its Applications)

Rings Close to Regular (Mathematics and Its Applications)

Askar A. Tuganbaev

4.9/5 (20441 ratings)

Description: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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Rings Close to Regular (Mathematics and Its Applications). To get started finding Rings Close to Regular (Mathematics and Its Applications), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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ISBN: 9048161169

Description: 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Rings Close to Regular (Mathematics and Its Applications). To get started finding Rings Close to Regular (Mathematics and Its Applications), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Rings Close to Regular (Mathematics and Its Applications)

Rings Close to Regular (Mathematics and Its Applications)

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