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Preface

Total Quotient Rings / I.：

Preliminaries / 1.：

Property A / 2.：

Zero-Dimensional Rings / 3.：

Compactness of Min R / 4.：

Notes

Valuation Theory / II.：

Valuations / 5.：

Prufer Rings / 6.：

Marot Rings / 7.：

Krull Rings / 8.：

Integral Closure / III.：

Integral Closure as Intersections / 9.：

Krull Rings II / 10.：

Integral Closure of Noetherian Rings / 11.：

Integral Closure of Noetherian Rings II / 12.：

When Polynomials Rings Are Integrally Closed / 13.：

Overrings of Polynomial Rings / IV.：

Properties of R(X) / 14.：

Principal Ideals and Pic R(X) / 15.：

When R(X) Is Integrally Closed / 16.：

The Ring R[less than sign]X[greater than sign] / 17.：

Divisibility in R[less than sign]X[greater than sign] and R(X) / 18.：

Multiplicatively Closed Subsets of R[X] / 19.：

Kronecker Function Rings / 20.：

Kronecker Function Rings and R(X) / 21.：

Kronecker Function Rings and R[X] [subscript (u subscript 2)] / 22.：

Chained Rings / V.：

Homomorphic Images of Valuation Domains / 23.：

Constructions and Examples / VI.：

Idealization / 25.：

A + B rings / 26.：

Examples / 27.：

Index of Main Results

Bibliography

Index

Preface

Total Quotient Rings / I.：

Preliminaries / 1.：

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Preliminaries / 1：

AR sequences and irreducible morphisms / 2：

Isolated singularities / 3：

Auslander categories / 4：

AR quivers / 5：

The Brauer-Thrall theorem / 6：

Matrix factorizations / 7：

Simple singularities / 8：

One-dimensional Cm rings of finite representation type / 9：

McKay graphs / 10：

Two-dimensional CM rings of finite representation type / 11：

KnÃ·rrer's periodicity / 12：

Grothendieck groups / 13：

CM modules on quadrics / 14：

Graded CM modules on graded CM rings / 15：

CM modules on toric singularities / 16：

Homogeneous CM rings of finite representation type / 17：

Addenda

References

Preliminaries / 1：

AR sequences and irreducible morphisms / 2：

Isolated singularities / 3：

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