LEADER 04868nam 2200649 a 450 001 9910455611003321 005 20200520144314.0 010 $a1-282-76146-3 010 $a9786612761461 010 $a981-4287-25-3 035 $a(CKB)2490000000001658 035 $a(EBL)3050897 035 $a(OCoLC)612404492 035 $a(SSID)ssj0000414141 035 $a(PQKBManifestationID)11302308 035 $a(PQKBTitleCode)TC0000414141 035 $a(PQKBWorkID)10393816 035 $a(PQKB)11499901 035 $a(MiAaPQ)EBC3050897 035 $a(WSP)00000589 035 $a(Au-PeEL)EBL3050897 035 $a(CaPaEBR)ebr10422335 035 $a(CaONFJC)MIL276146 035 $a(EXLCZ)992490000000001658 100 $a20090505d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aClassical artinian rings and related topics$b[electronic resource] /$fYoshitomo Baba, Kiyoichi Oshiro 210 $a[Hackensack], N.J. $cWorld Scientific$dc2009 215 $a1 online resource (310 p.) 300 $aDescription based upon print version of record. 311 $a981-4287-24-5 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; List of Symbols; 1. Preliminaries; 1.1 Background Sketch; 1.2 Semiperfect Rings and Perfect Rings; 1.3 Frobenius Algebras, and Nakayama Permutations and Nakayama Automorphisms of QF-Rings; 1.4 Notation in Matrix Representations of Rings; COMMENTS; 2. A Theorem of Fuller; 2.1 Improved Versions of Fuller's Theorem; 2.2 M-Simple-Injective and Quasi-Simple-Injective Modules; 2.3 Simple-Injectivity and the Condition r[e, g, f]; 2.4 ACC on Right Annihilator Ideals and the Condition r[e, g, f]; 2.5 Injectivity and Composition Length; COMMENTS; 3. Harada Rings 327 $a5.2 Self-Duality and Almost Self-Duality of Left Harada Rings5.3 Koike's Example of a QF-Ring without a Nakayama Automorphism; 5.4 Factor Rings of QF-Rings with a Nakayama Automorphism; COMMENTS; 6. Skew Matrix Rings; 6.1 Definition of a Skew Matrix Ring; 6.2 Nakayama Permutations vs Given Permutations; 6.3 QF-Rings with a Cyclic Nakayama Permutation; 6.4 Strongly QF-Rings; 6.5 Block Extensions of Skew Matrix Rings; COMMENTS; 7. The Structure of Nakayama Rings; 7.1 Kupisch Series and Kupisch Well-Indexed Set via Left HRings; 7.2 Nakayama QF-Rings; 7.3 A Classification of Nakayama Rings 327 $a7.4 An Example of a Nakayama QF-Ring of KNP(1 ! 1)-Type7.5 The Self-Duality of Nakayama Rings; COMMENTS; 8. Modules over Nakayama Rings; 8.1 Characterizations of Nakayama Rings by Lifting and Extending Properties; COMMENTS; 9. Nakayama Algebras; 9.1 Nakayama Algebras over Algebraically Closed Fields; 9.2 Nakayama Group Algebras; COMMENTS; 10. Local QF-rings; 10.1 Local QF-rings; 10.2 Examples of Local QF-Rings with Radical Cubed Zero; COMMENTS; Open Questions; Bibliography; Index 330 $aQuasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since then, these classical artinian rings have continued to fascinate ring theorists with their abundance of properties and structural depth. In 1978, M Harada introduced a new class of artinian rings which were later called Harada rings in his honour. Quasi-Frobenius rings, Nakayama rings and Harada rings are very closely interrelated. As a result, from a new perspective, we may study the classical artinian rings through their interaction and overlap with Harada rings. The objective of this seminal work is to present the structure of Harada rings and provide important applications of this structure to the classical artinian rings. In the process, we cover many topics on artinian rings, using a wide variety of concepts from the theory of rings and modules. In particular, we consider the following topics, all of which are currently of much interest and ongoing research : Nakayama permutations, Nakayama automorphisms, Fuller's theorem on i-pairs, artinian rings with self-duality, skew-matrix rings, the classification of Nakayama rings, Nakayama group algebras, the Faith conjecture, constructions of local quasi-Frobenius rings, lifting modules, and extending modules. In our presentation of these topics, the reader will be able to retrace the history of artinian rings. 606 $aArtin rings 606 $aCommutative rings 606 $aRings (Algebra) 608 $aElectronic books. 615 0$aArtin rings. 615 0$aCommutative rings. 615 0$aRings (Algebra) 676 $a512/.4 700 $aBaba$b Yoshitomo$0870615 701 $aO?shiro$b Kiyoichi$f1943-$0870616 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910455611003321 996 $aClassical artinian rings and related topics$91943476 997 $aUNINA