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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aBasic Representation Theory of Algebras /$fby Ibrahim Assem, Flávio U. Coelho
205   $a1st ed. 2020.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020.
215   $a1 online resource (X, 311 p. 288 illus.)
225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v283
311   $a3-030-35117-3 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- 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.
330   $aThis textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander-Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.
410  0$aGraduate Texts in Mathematics,$x0072-5285 ;$v283
606   $aAssociative rings
606   $aRings (Algebra)
606   $aCategories (Mathematics)
606   $aAlgebra, Homological
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
615  0$aAssociative rings.
615  0$aRings (Algebra)
615  0$aCategories (Mathematics)
615  0$aAlgebra, Homological.
615 14$aAssociative Rings and Algebras.
615 24$aCategory Theory, Homological Algebra.
676   $a512.9
700   $aAssem$b Ibrahim$4aut$4http://id.loc.gov/vocabulary/relators/aut$01020549
702   $aCoelho$b Flávio U$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910485037103321
996   $aBasic Representation Theory of Algebras$92413546
997   $aUNINA