Overview
- Provides the first systematic treatment of formal matrices in a single volume
- Examines injective, flat, projective and hereditary modules over formal matrix rings of order 2 in great detail
- Includes concrete examples that illustrate the structures of formal matrix rings
- Includes supplementary material: sn.pub/extras
Part of the book series: Algebra and Applications (AA, volume 23)
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Table of contents (5 chapters)
Keywords
About this book
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.
Reviews
“The book is written in a friendly style. The presentation is clear and many good examples are given to illustrate the main concepts and results. The book is useful to researchers in ring theory and linear algebra. It is also suitable for graduate students.” (Sorin Dascalescu, zbMATH 1367.16001, 2017)
Authors and Affiliations
Bibliographic Information
Book Title: Formal Matrices
Authors: Piotr Krylov, Askar Tuganbaev
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/978-3-319-53907-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-53906-5Published: 07 April 2017
Softcover ISBN: 978-3-319-85272-0Published: 25 July 2018
eBook ISBN: 978-3-319-53907-2Published: 30 March 2017
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: VIII, 156
Topics: Associative Rings and Algebras, Category Theory, Homological Algebra, K-Theory, Linear and Multilinear Algebras, Matrix Theory