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930107s1993 enka b 00100 eng |
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|a 9817611
|5 LACONCORD2021
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|a 0521410681
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|a (OCoLC)27339590
|5 LACONCORD2021
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|a QA251.38
|b .B78 1993
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|a 512/.4
|2 20
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|a Bruns, Winfrid,
|d 1946-
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|a Cohen-Macaulay rings /
|c Winfrid Bruns, Jurgen Herzog.
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| 260 |
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|a Cambridge [England] ;
|a New York :
|b Cambridge University Press,
|c 1993.
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| 300 |
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|a xi, 403 p. :
|b ill. ;
|c 24 cm.
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| 440 |
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|a Cambridge studies in advanced mathematics ;
|v 39
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| 504 |
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|a Includes bibliographical references (p. 374-389) and index.
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|a 1. Regular sequences and depth. 1.1. Regular sequences. 1.2. Grade and depth. 1.3. Depth and projective dimension. 1.4. Some linear algebra. 1.5. Graded rings and modules. 1.6. The Koszul complex -- 2. Cohen-Macaulay rings. 2.1. Cohen-Macaulay rings and modules. 2.2. Regular rings and normal rings. 2.3. Complete intersections -- 3. The canonical module. Gorenstein rings. 3.1. Finite modules of finite injective dimension. 3.2. Injective hulls. Matlis duality. 3.3. The canonical module. 3.4. Gorenstein ideals of grade 3. Poincare duality. 3.5. Local cohomology. The local duality theorem. 3.6. The canonical module of a graded ring -- 4. Hilbert functions and multiplicities. 4.1. Hilbert functions of graded modules. 4.2. Macaulay's theorem on Hilbert functions. 4.3. Further constraints on Hilbert functions. 4.4. Filtered rings. 4.5. The Hilbert-Samuel function and reduction ideals. 4.6. The multiplicity symbol -- 5. Stanley-Reisner rings. 5.1. Simplicial complexes. 5.2. Polytopes.
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|a 5.3. Local cohomology of Stanley-Reisner rings. 5.4. The upper bound theorem. 5.5. Gorenstein complexes. 5.6. The canonical module of a Stanley-Reisner ring -- 6. Semigroup rings and invariant theory. 6.1. Affine semigroup rings. 6.2. Local cohomology of affine semigroup rings. 6.3. Normal semigroup rings. 6.4. Invariants of tori and finite groups. 6.5. Invariants of linearly reductive groups -- 7. Determinantal rings. 7.1. Graded Hodge algebras. 7.2. Straightening laws on posets of minors. 7.3. Properties of determinantal rings -- 8. Big Cohen-Macaulay modules. 8.1. The annihilators of local cohomology. 8.2. The Frobenius functor. 8.3. Modifications and non-degeneracy. 8.4. Hochster's finiteness theorem. 8.5. Balanced big Cohen-Macaulay modules -- 9. Homological theorems. 9.1. Grade and acyclicity. 9.2. Regular rings as direct summands. 9.3. Canonical elements in local cohomology modules. 9.4. Intersection theorems. 9.5. Ranks of syzygies. 9.6. Bass numbers.
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|a Appendix: A summary of dimension theory.
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|a Cohen-Macaulay rings.
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|a Herzog, Jurgen.
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