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Formal matrices

Krylov, Piotr.

Formal matrices

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Formal matricesby Piotr Krylov, Askar Tuganbaev.
作者:	Krylov, Piotr.
其他作者:	Tuganbaev, Askar.
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	viii, 156 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Matrices.
電子資源:	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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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.
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