CONTENTS -- PREFACE -- On Harada Rings of a Component Type Yoshitomo Baba -- 1. Introduction. -- 2. Preliminaries -- 3. Structure of Harada rings of a component type -- 4. Self-duality of Harada ring of a component type -- Acknowledgements -- References -- Ring Hulls of Extension Rings Gary F. Birkenmeier, Jae Keol Park and S. Tariq Rizvi -- Acknowledgments. -- References -- Constructing Morphic Rings Jianlong Chen, Yuanlin Li and Yiqiang Zhou -- ACKNOWLEDGEMENTS -- References -- Some Properties of Additive Endomorphisms and Maps on Groups Yong Uk Cho -- 1. Introduction -- 2. Results -- References -- Locally Semi-T-nilpotent Families of Modules John Clark -- 1. The definition and introduction -- 2. Decompositions which complement summands -- 3. The exchange property -- 4. Extending modules -- 5. Lifting, quasi-discrete and discrete modules -- 6. Final remarks -- Acknowledgments -- References -- Smooth Algebras and their Applications Charudatta R. Hajarnavis -- 1. Introduction -- 2. Preliminaries and Background -- 3 Stably Free Ideals -- 3.1 Lemma [3, Proposition 1.8]: -- 3.2 Corollary [3, Proposition 1.14] -- 3.3 Proposition: -- 3.4 Theorem: -- 3.5 Lemma: -- 3.6 Lemma: -- 3.7 Corollary: -- 3.8 Theorem: -- 4 Symbolic Powers -- 4.1 Lemma: -- 4.2 Theorem [4, TheoremlS]: -- 4.3 Theorem [4, Theoreml6J: -- 4.4 Corollary [4, Theoreml7]: -- References -- Rings whose Simple Modules have some Properties Yasuyuki Hirano -- 1. Projectivity of simple modules -- 2. Flatness of simple modules -- 3. Injectivity of simple modules -- 4. Semiartinian rings and max rings -- 5. -V rings -- 6. Rings whose modules of finite length are semisimple -- References -- On a Finitely Generated P-injective Left Ideal Yasuyuki Hirano and Jin Yong Kim -- ACKNOWLEDGMENTS -- References -- Crossed Products and Fully Prime Rings Liujia Huang and Zhong Yi -- References.

On a Left H-Ring with Nakayama Automorphism Jiro Kado -- 1 Nakayama isomorhphism -- References -- Isomorphism Classes of Algebras with Radical Cube Zero /. Kikumasa and H. Yoshimura -- Introduction -- 1. Matrix Congruence -- 2. k-algebras of Type (l,n, 1) -- 3. k-algebras of Type (1, 2,1) -- Acknowledgments -- References -- On Lifting Properties of Modules Yosuke Kuratomi -- 1. Preliminaries -- 2. Classical Artinian Rings -- 3. Generalized Projectivity -- 4. Direct sums of lifting modules -- 5. Lifting modules over right perfect rings -- References -- On Regular Rings with the Property (DF) Mamoru Kutami -- 1. Preliminaries -- 2. Regular Rings with S-comparability -- 3. Weak Comparability -- 4. New Constructions -- References -- Semilattice Graded Weak Hopf Algebra and its Quantum Double Fang Li and Haijun Cao -- 1. Decomposition -- 2. Structure Of Quantum Double -- References -- Notes on FP-projective Modules and FP-injective Modules Lixin Mao and Nanqing Ding -- 1. Introduction -- 2. Results -- Acknowledgments -- References -- A Survey of Morphic Modules and Rings W. K. Nicholson -- Abstract -- 1. MORPHIC MODULES -- 2. ENDOMORPHISM RINGS -- 3. LEFT SPECIAL RINGS -- 4. MATRIX RINGS -- 5. STRUCTURE THEOREMS -- 6. INTERNAL CANCELLATION -- References -- Clean Rings: A Survey W. K. Nicholson and Yiqiang Zhou -- 1. Connections with other notions -- 2. Clean endomorphism rings -- 3. The center of a clean ring -- 4. Strongly clean rings -- 5. Uniquely clean rings -- 6. Group rings -- 7. The extension questions of clean and strongly clean rings -- 8. Semiboolean rings -- 9. Connections with C*-Algebras and clean rings of continuous functions -- References -- Flat Cover and Cotorsion Envelope Commute Phillip Rothmaler -- 1. Introduction -- 2. The result -- References.

A Generalization of the DeMeyer Theorem for Central Galois Algebras George Szeto and Lianyong Xue -- 1. Introduction -- 2. Basic Definitions and Notations -- 3. Galois Extensions -- Acknowledgments -- References -- Weak Krull Dimension over Commutative Rings Gaohua Tang -- 1. Introduction -- 2. Definitions and Examples -- 3. A Characterization of Regular Coherent Local Rings -- 4. A Generalization of Serre's Theorem -- References -- Baer Property of Modules and Applications S. Tariq Rizvi and Cosmin S. Roman -- 1. Introduction and Preliminaries -- 2. Baer Rings -- 3. Baer Modules -- 4. Connections to Extending Property -- 5. Applications -- Open Questions -- References -- Properties of Graded Formal Triangular Matrix Rings Yao Wang and Y. L. Ren -- 1. Introduction -- 2. Graded Regularity -- 3. Graded Jacobson Radical -- 4. Graded Direct Finiteness -- References -- Power-substitution and Exchange Rings Jiaqun Wei -- 1. Introduction -- 2. The power-substitution property -- 3. The unit power-substitution property -- References -- From Galois Field Extensions to Galois Comodules Robert Wisbauer -- I. Preliminaries -- 1.1. Algebras and modules. -- 1.2. Coalgebras and comodules. -- 1.3. Bialgebras and Hopf modules. -- 1.4. Group algebras and their dual. -- 1.5. Comodule algebras and relative Hopf modules. -- 1.6. Corings and comodules. -- 1.7. A as a C-comodule. -- 1.8. Coring of a projective module. -- 1.9. The Sweedler coring. -- 1.10. Entwining structures. -- 1.11. Bialgebras and corings -- 1.12. Comodule algebras and corings -- 1.13. Cointegrals. -- 1.14. Relative injectivity. -- 1.15. Fully -- 2. Galois extensions and comodules -- 2.1. Galois Reid extension. -- 2.2. Comodule algebras. -- 2.3. Coalgebra-Galois extensions. -- 2.4. Galois corings. -- 2.5. Hopf algebras. -- 2.6. Galois comodules. -- 3. General Galois comodules -- 3.1. Galois comodules.

3.2. Isomorphisms for Galois comodules. -- 3.3. (C, .A)-injective modules. -- 3.4. Module properties of sP. -- 3.5. Semisimple Galois comodules. -- 3.6. Galois comodules with PA f.g. -- 3.7. Strongly (C, A)-injective Galois comodules. -- 3.8. Equivalences. Let P £ M.c -- 3.9. Remarks. -- References -- On the Finitistic Dimension Conjecture Changchang Xi -- 1. A brief recall of the history -- 2. Connection with other conjectures -- 3. Some known results -- 4. Some new results -- 4.1. General question -- 4.2. New results -- 4.3. Remarks -- 4.4. Examples -- 4.5. Some results on representation dimension -- 5. Some Open questions -- Acknowledgments -- References -- Galois Coverings of Selfinjective Algebras by Twisted Repetitive Algebras Kunio Yamagata -- 1. Introduction -- 2. Coverings -- 2.1. Locally bounded categories -- 2.2. Covering functors -- 2.3. Repetitive categories -- 3. Positive Galois coverings -- 3.1. Periodic categories -- 3.2. Positive Galois coverings of self-injective algebras -- 4. Criterion Theorems -- References -- The Clebsch-Gordan Decomposition for Quantum Algebra Shilin Yang and Hong Wang -- Introduction -- 1. Finite dimensional integrable highest weight modules -- 2. The Clebsch-Gordan decomposition -- References -- Computation of the Projective Dimension of Finitely Generated Modules over Polynomial Rings Zhong Yi -- 1. introduction -- 2. Main Results -- Acknowledgments -- References.