Formal Matrices
Seiten
2017
|
1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-53906-5 (ISBN)
Springer International Publishing (Verlag)
978-3-319-53906-5 (ISBN)
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.
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.
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 book is an attempt to give a rather comprehensive treatment of formal matrix rings. ... I strongly recommend this book; it should definitely be in every serious university's library." (Leon Van Wyk, Mathematical Reviews, November, 2017)
"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)
| Erscheinungsdatum | 19.04.2017 |
|---|---|
| Reihe/Serie | Algebra and Applications |
| Zusatzinfo | VIII, 156 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Algebra • algebraic topology • Associative rings and algebras • Category Theory, Homological Algebra • Determinant • flat module • formal matrix • generalized matrix • Grothendieck group • injective module • K-theory • Linear and Multilinear Algebras, Matrix Theory • Mathematical Foundations • Mathematics • mathematics and statistics • matrix theory • Morita context • projective module • Ring Theory • Whitehead group |
| ISBN-10 | 3-319-53906-X / 331953906X |
| ISBN-13 | 978-3-319-53906-5 / 9783319539065 |
| Zustand | Neuware |
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