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Formal matrices

Krylov, Piotr.

Formal matrices

Record Type:	Electronic resources : Monograph/item
Title/Author:	Formal matricesby Piotr Krylov, Askar Tuganbaev.
Author:	Krylov, Piotr.
other author:	Tuganbaev, Askar.
Published:	Cham :Springer International Publishing :2017.
Description:	viii, 156 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Matrices.
Online resource:	http://dx.doi.org/10.1007/978-3-319-53907-2
ISBN:	9783319539072$q(electronic bk.)

Formal matrices
Krylov, Piotr.

Formal matrices[electronic resource] /by Piotr Krylov, Askar Tuganbaev. - Cham :Springer International Publishing :2017. - viii, 156 p. :ill., digital ;24 cm. - Algebra and applications,v.231572-5553 ;. - Algebra and applications ;v.17..

Introduction -- Construction of Formal Matrix Rings of Order 2 -- Modules over Formal Matrix Rings -- Formal Matrix Rings over a Given Ring -- Grothendieck and Whitehead Groups of Formal Matrix Rings.

This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.

ISBN: 9783319539072$q(electronic bk.)

Standard No.: 10.1007/978-3-319-53907-2doiSubjects--Topical Terms:

181876
Matrices.

LC Class. No.: QA188

Dewey Class. No.: 512.9434

Formal matrices
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100 1 $a Krylov, Piotr. $3 776027
245 1 0 $a Formal matrices $h [electronic resource] / $c by Piotr Krylov, Askar Tuganbaev.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2017.
300 $a viii, 156 p. : $b ill., digital ; $c 24 cm.
490 1 $a Algebra and applications, $x 1572-5553 ; $v v.23
505 0 $a Introduction -- Construction of Formal Matrix Rings of Order 2 -- Modules over Formal Matrix Rings -- Formal Matrix Rings over a Given Ring -- Grothendieck and Whitehead Groups of Formal Matrix Rings.
520 $a This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.
650 0 $a Matrices. $3 181876
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Category Theory, Homological Algebra. $3 275954
650 2 4 $a K-Theory. $3 277863
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 274063
700 1 $a Tuganbaev, Askar. $3 776028
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Algebra and applications ; $v v.17. $3 558850
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-53907-2
950 $a Mathematics and Statistics (Springer-11649)