دانلود کتاب International Symposium on Ring Theory

Ring theory provides the algebraic underpinnings for many areas of mathematics, computer science, and physics. For example, ring theory appears in: functional analysis; algebraic topology; algebraic number theory; coding theory; and in the study of quantum theory. This volume is a collection of research papers, many presented at the 3rd Korea-China-Japan International Symposium on Ring Theory held jointly with the 2nd Korea-Japan Ring Theory Seminar, in Korea, The articles examine wide-ranging developments and methodologies in various areas, including classical Hopf algebras and quantum groups.

Cover

Trends in Mathematics

International Symposiumon Ring Theory

Copyright

© 2001 Springer Science+Business Media

ISBN 978-1-4612-6650-1

QA247.I58 2000 512'.4-Hdc21

ISBN 978-1-4612-0181-6 (eBook)

DOI 10.1007/978-14612-0181-6

SP1N 1 0 7 4 8 5 5 3

To all Ring Theorists-past, present, and future

Contents

Preface

Acknowledgments

Participants

Generalized Deviations of Posets with Applications to Chain Conditions on Modules

1. Introduction

2. Terminology and Notation

3. Generalized Deviation of Posets

4. \Gamma -Deviation of Modular Lattices

5. The Double Infinite Chain Condition and Balanced Krull Dimension

6. Applications to Modules and Grothendieck Categories

References

Stability Properties of Exchange Rings

0. Introduction

1. Definition and Examples

2. Stable Rank

3. Separativity

4. Stability Properties of Exchange Rings

References

Good Conditions for the Total

1. Introduction

2. Good Condition for the Total

3. The Inverse Problem

References

Semicentral Reduced Algebras

0. Introduction

1. Preliminaries and Motivations

2. Matrix Algebras

3. Semicentral Reduced Rings with Additional Conditions

References

On Generalizations of Injectivity

1. Introduction

2. Simple-injectivity

3. Mininjectivity

4. GP-injectivity

References

A uslander-Gorenstein Rings for Beginners

1. Introduction

2. Filtered Rings and Graded Rings

3. Minimal Injective Resolutions and Cohen-Macaulay Rings

4. Catenarity

5. n-Gorenstein Rings

6. Duality

7. Quantum Group Examples

8. Tailpiece

References

The Flat Cover Conjecture and Its Solution

Abstract

References

Some Results on Skew Polynomial Rings over a Reduced Ring

0. Introduction

1. Some Conditions for R[x; \sigma] to be Reduced

2. Conditions for R[x; \sigma] to be Baer, quasi-Baer or p.q.-Baer

Acknowledgements

References

Derived Equivalences and Tilting Theory

1. Preliminaries

2. Hereditary Categ

3. Basic Examples and their Characterization

4. Hochschild Cohomology

References

CS-Property of Direct Sums of Uniform Modules

1. Preliminaries

2. Main Theorem

References

Generalized Principally Injective Maximal Ideals

Abstract

References

The Module of Differentials of a Noncommutative Ring Extension

Abstract

1. Central Derivations and One-Sided Derivations

2. Module of Differentials

3. Elementary Properties of Modules of Differentials

4. Quasi-Separable Extensions

References

Dual Bimodules and Nakayama Permutations

Abstract

References

The Coinduced Functor and Homological Properties of Hopf Modules

Abstract

0. Introduction

1. Preliminaries

2. The Functor HOM

3. The Coinduced Functor HOMB(A, -)

References

Hopf Algebra Coaction and Its Application to Group-Graded Rings

Abstract

0. Introduction

1. A Morita Context Connection between A^coH and A#H^*rat

2. Application to G-Graded Algebras

References

Non-Commutative Valuation Rings and Their Global Theories

Abstract

1. Non-Commutative Valuation Rings

2. Priifer Orders and Semi-hereditary Orders

References

On the Maximal t-Corational Extensions of Modules

Abstract

1. t-Corational Extensions of Modules

2. The Maximal t-Corational Extensions.

3. Applications

References

On Values of Cyclotomic Polynomials

Abstract

1. Introduction

2. Cipher

References

Generalized Jordan Derivations

Abstract

0. Introduction

1. Preliminaries

2. Elementary Properties of Generalized Jordan and Lie Derivations

3. Other Results of Generalized Jordan Derivations

References

On Quasi-Frobenius Rings

Abstract

1. Preliminaries

2. FP-Injective Rings

3. FP-Rings

4. The C2-Condition

5. The Faith-Menal Conjecture

References

Theories of Harada in Artinian Rings and Applications to Classical Artinian Rings

Abstract

1. Introduction

2. Fuller's Theorem

3. Harada Rings

4. Nakayama Rings

5. Skew Matrix Rings

6. QF-Nakayama Rings

7. Self-duality of Left H-rings

8. Kupisch's Work

References

On Some Dimensions of Modular Lattices and Matroids

Abstract

0. Introduction

1. Preliminaries

2. A Matroid Related to the Goldie Dimension of Modular Lattices

3. A Matroid Related to the Kuros-Ore Dimension of Modular Lattices

4. A Relation between the Goldie Dimension and the Length

References

On Torsion-free Modules over Valuation Domains

Abstract

1. Introduction

2. Preliminaries

3. A Special Pull-back Diagram

4. The n-Balanced Submodules and Modules with Finite bpd

5. Nn-Families

6. The Global Balanced-Projective Dimension

7. Butler Modules

References

Heeke Orders, Cellular Orders and Quasi-Hereditary Orders

Abstract

1. Introduction

2. The Hecke Order H_S3 of the Symmetric Group S3

3. Heeke Orders of Rank 2 BN-Pairs

4. Orders

5. The Cell Structure of ZS3 and 'H_S3

6. Cellular Orders

7. Extensions of the Cell Modules for the Heeke Orders of Dihedral Groups

9. Quasi-Hereditary Rings

10. A Separable Deformation of ZS3

11. Separable and Maximal Deformations

12. Localizations of H_S3 and Z3S3

13. Green Rings - Graph Rings

14. A Characterization of Graph Orders

15. Cohen-Macaulay Modules over Two-dimensional Green Orders

References

Some Kind of Duality

Abstract

1. Preliminaries

2. Reflexive Modules

3. Chain Conditions

References

On Inertial Subalgebras of Certain Rings

Abstract

References

Some Recent Results on Hopficity, Co-hopficity and Related Properties

Abstract

1. Introduction

2. Hopficity and co-Hopficity in Some Familiar Categories

3. Hopfian and co-Hopfian Zero Dimensional Spaces

4. Residual Finiteness in Rings and Modules

5. Determining Co-hopfian Surface Groups and Algebraic Consequences

6. Hopficity of Polynomial Rings and Product Rings

7. Some Open Problems

References

Some Studies on QcF -coalgebras

Abstract

1. Introduction

2. Some Characterizations

3. The Uniqueness of Integrals for QcF-coalgebras

4. QcF -coalgebras and Equivalences

References

Finitely Pseudo -Frobenius Rings

Abstract

Introduction

Notation and Terminology

1. Results on FPF rings after Faith-Page [FaiPa]

1.1. Semiperfect FPF Rings

1.2. Noetherian FPF Rings

1.3. (Von Neumann) Regular FPF Rings

1.4. N onsingular FPF Rings

1.5. Commutative FPF Rings

1.6. Problems in [FaiPa] and Others

1.6.1. When is a Trivial Extension R ~ M of a Ring R by anR-bimodule M FPF?

1.6.2. Is the Center of an FPF Ring FPF?

1.6.3. Characterize FPF Group Rings

1.6.4. Is a Nonsingular FPF Ring Semihereditary?

1.6.5. Is there an FPF Ring R with G a Finite Group of Automorphisms of R whose Galois Subring RG (= {r E R I g(r) = r (g E Gn) is not FPF?

1.6.6. Other Topics

2. Triangular Matrix FPF Rings

Acknowledgements.

References

Surjectivity of Linkage Maps

Abstract

1. Introduction

2. Main Results

References

Infinite Quivers and Cohomology Groups

Abstract

1. Preliminaries

2. Cohomology Groups ExtAe(A, A)

3. Monomial Algebras

4. Vanishing of the First Hochschild Cohomology

References

Open Problems

Pere Ara

Yoshitomo Baba

Gary F. Birkenmeier, Jae Keol Park and Jin Yong Kim

Yasuyuki Hirano

Hidetoshi Marubayashi

Kaoru Motose

w. K. Nicholson and M. F. Yousif

K. M. Rangaswamy

s. Tariq Rizvi

References

Mingyi Wang

References

Alexander Zimmermann