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Field name	Details
Dewey Class	512.46
Title	Basic Representation Theory of Algebras ([EBook]) / by Ibrahim Assem, Flávio U. Coelho.
Author	Assem, Ibrahim
Added Personal Name	Coelho, Flávio U.
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2020.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2020.
Physical Details	X, 311 p. 288 illus. : online resource.
Series	Graduate texts in mathematics 0072-5285 ; ; 283
ISBN	9783030351182
Summary Note	This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander-Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.:
Contents note	Introduction -- Chapter 1: Modules, algebras and quivers -- Chapter 2: The radical and almost split sequences -- Chapter 3: Constructing almost split sequences -- Chapter 4: The Auslander-Reiten quiver of an algebra -- Chapter 5: Endomorphism algebras -- Chapter 6: Representation-finite algebras -- Bibliography -- Index.
Mode of acces to digital resource	Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-35118-2
Links to Related Works	Subject References: Associative rings . Associative Rings and Algebras . Category Theory, Homological Algebra . Category theory (Mathematics) . Homological algebra . Rings (Algebra) . Authors: Assem, Ibrahim . author . Coelho, Flávio U. . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 512.46 .

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Basic Representation Theory of Algebras

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