03108nam 2200589 450 991078887200332120180613001259.01-4704-0831-7(CKB)3360000000464592(EBL)3113966(SSID)ssj0000889284(PQKBManifestationID)11478617(PQKBTitleCode)TC0000889284(PQKBWorkID)10875650(PQKB)11431871(MiAaPQ)EBC3113966(RPAM)1508137(PPN)195412915(EXLCZ)99336000000046459220140905h19891989 uy 0engur|n|---|||||txtccrTwo-dimensional tame and maximal orders of finite representation type /Idun Reiten and Michel Van den BerghProvidence, Rhode Island, United States :American Mathematical Society,1989.©19891 online resource (85 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 80, Number 408"July 1989, Volume 80, Number 408 (fourth of 5 numbers)"--Cover.0-8218-2469-4 Includes bibliographical references.""TABLE OF CONTENTS""; ""INTRODUCTION""; ""1. TAME AND MAXIMAL ORDERS AND THEIR GROTHENDIECK GROUPS""; ""1.1 Orders""; ""1.2 Reflexive Morita equivalence""; ""1.3 Grothendieck group of tame and maximal orders""; ""2. THE ASSOCIATED GRADED ORDERS""; ""2.1 The shape of the Auslander-Reiten quivers""; ""2.2 The associated graded algebras""; ""2.3 The isomorphism classes of the path algebras with quadratic relations""; ""2.4 Properties of the path algebras with quadratic relations and their completions""; ""2.5 The classification for gr Î?""; ""2.6 k[[x[sub(1)],x[sub(2)]]]-algebras""""2.7 General comments on existence of almost split sequences""""3. THE LATTICE OF OVERLYING ORDERS""; ""3.1 The Grothendieck group of a translation quiver""; ""3.2 Admissible sets and zero sets""; ""3.3 Zero sets of tame orders""; ""3.4 When are Î? and End [sub(Î?)] (M) reflexive Morita equivalent?""; ""3.5 AR-quivers for overorders""; ""3.6 Relationship between K[sub(0)](mod[sub(1)] Î?) and K[sub(0)](mod Î?)""; ""4. MAXIMAL ORDERS OF FINITE REPRESENTATION TYPE""; ""4.1 The method""; ""4.2 The universal covering of Î? is ZD[sub(n)]""; ""4.3 The universal covering is ZE[sub(i)]""Memoirs of the American Mathematical Society ;Volume 80, Number 408.Associative algebrasRepresentations of algebrasGrothendieck groupsAssociative algebras.Representations of algebras.Grothendieck groups.512/.24Reiten Idun1942-55368Bergh M. van denMiAaPQMiAaPQMiAaPQBOOK9910788872003321Two-dimensional tame and maximal orders of finite representation type3705591UNINA