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＜E-Book＞
Formal Matrices / by Piotr Krylov, Askar Tuganbaev
(Algebra and Applications. ISSN:21922950 ; 23)

Edition	1st ed. 2017.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2017
Size	VIII, 156 p : online resource
Authors	*Krylov, Piotr author Tuganbaev, Askar author SpringerLink (Online service)
Subjects	LCSH:Associative rings LCSH:Associative algebras LCSH:Algebra, Homological LCSH:K-theory LCSH:Algebras, Linear FREE:Associative Rings and Algebras FREE:Category Theory, Homological Algebra FREE:K-Theory FREE:Linear Algebra
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-319-53907-2

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