|
|
|
|
| LEADER |
00000pam a22000004a 4500 |
| 001 |
4315195 |
| 003 |
ICU |
| 005 |
20241119165449.9 |
| 008 |
000426s2000 gw b 001 0 eng |
| 010 |
|
|
|a 00032970
|
| 020 |
|
|
|a 3540666419 (alk. paper)
|
| 035 |
|
|
|a 32970
|
| 040 |
|
|
|a DLC
|c DLC
|d DLC
|d NhCcYBP
|d OrLoB-B
|d OCoLC
|
| 041 |
1 |
|
|a eng
|h fre
|
| 042 |
|
|
|a pcc
|
| 050 |
0 |
0 |
|a QA564
|b .S4313 2000
|
| 082 |
0 |
0 |
|a 516.3/5
|2 21
|
| 100 |
1 |
|
|a Serre, Jean Pierre,
|d 1926-
|1 http://viaf.org/viaf/66473477
|
| 240 |
1 |
0 |
|a Algèbre locale, multiplicités.
|l English
|
| 245 |
1 |
0 |
|a Local algebra /
|c Jean-Pierre Serre ; translated from the French by CheeWhye Chin.
|
| 260 |
|
|
|a Berlin ;
|a New York :
|b Springer,
|c c2000.
|
| 300 |
|
|
|a xiii, 128 p. ;
|c 25 cm.
|
| 336 |
|
|
|a text
|b txt
|2 rdacontent
|0 http://id.loc.gov/vocabulary/contentTypes/txt
|
| 337 |
|
|
|a unmediated
|b n
|2 rdamedia
|0 http://id.loc.gov/vocabulary/mediaTypes/n
|
| 338 |
|
|
|a volume
|b nc
|2 rdacarrier
|0 http://id.loc.gov/vocabulary/carriers/nc
|
| 440 |
|
0 |
|a Springer monographs in mathematics,
|x 1439-7382
|
| 504 |
|
|
|a Includes bibliographical references (p. [123]-126) and indexes.
|
| 505 |
0 |
0 |
|g I.
|t Prime Ideals and Localization.
|g 1.
|t Notation and definitions.
|g 2.
|t Nakayama's lemma.
|g 3.
|t Localization.
|g 4.
|t Noetherian rings and modules.
|g 5.
|t Spectrum.
|g 6.
|t The noetherian case.
|g 7.
|t Associated prime ideals.
|g 8.
|t Primary decompositions --
|g II.
|t Tools.
|g A.
|t Filtrations and Gradings.
|g 1.
|t Filtered rings and modules.
|g 2.
|t Topology defined by a filtration.
|g 3.
|t Completion of filtered modules.
|g 4.
|t Graded rings and modules.
|g 5.
|t Where everything becomes noetherian again - q-adic filtrations.
|g B.
|t Hilbert-Samuel Polynomials.
|g 1.
|t Review on integer-valued polynomials.
|g 2.
|t Polynomial-like functions.
|g 3.
|t The Hilbert polynomial.
|g 4.
|t The Samuel polynomial --
|g III.
|t Dimension Theory.
|g A.
|t Dimension of Integral Extensions.
|g 1.
|t Definitions.
|g 2.
|t Cohen-Seidenberg first theorem.
|g 3.
|t Cohen-Seidenberg second theorem.
|g B.
|t Dimension in Noetherian Rings.
|g 1.
|t Dimension of a module.
|g 2.
|t The case of noetherian local rings.
|g 3.
|t Systems of parameters.
|g C.
|t Normal Rings.
|g 1.
|t Characterization of normal rings.
|g 2.
|t Properties of normal rings.
|g 3.
|t Integral closure.
|g D.
|t Polynomial Rings.
|g 1.
|t Dimension of the ring A[X[subscript 1],...,X[subscript n]].
|g 2.
|t The normalization lemma.
|g 3.
|t Applications. I. Dimension in polynomial algebras.
|g 4.
|t Applications. II. Integral closure of a finitely generated algebra.
|g 5.
|t Applications. III. Dimension of an intersection in affine space --
|g IV.
|t Homological Dimension and Depth.
|g A.
|t The Koszul Complex.
|g 1.
|t The simple case.
|g 2.
|t Acyclicity and functorial properties of the Koszul complex.
|g 3.
|t Filtration of a Koszul complex.
|g 4.
|t The depth of a module over a noetherian local ring.
|g B.
|t Cohen-Macaulay Modules.
|g 1.
|t Definition of Cohen-Macaulay modules.
|g 2.
|t Several characterizations of Cohen-Macaulay modules.
|g 3.
|t The support of a Cohen-Macaulay module.
|g 4.
|t Prime ideals and completion.
|g C.
|t Homological Dimension and Noetherian Modules.
|g 1.
|t The homological dimension of a module.
|g 2.
|t The noetherian case.
|g 3.
|t The local case.
|g D.
|t Regular Rings.
|g 1.
|t Properties and characterizations of regular local rings.
|g 2.
|t Permanence properties of regular local rings.
|g 3.
|t Delocalization.
|g 4.
|t A criterion for normality.
|g 5.
|t Regularity in ring extensions.
|g App. I.
|t Minimal Resolutions --
|g App. II.
|t Positivity of Higher Euler-Poincare Characteristics --
|g App. III.
|t Graded-polynomial Algebras --
|g V.
|t Multiplicities.
|g A.
|t Multiplicity of a Module.
|g 1.
|t The group of cycles of a ring.
|g 2.
|t Multiplicity of a module.
|g B.
|t Intersection Multiplicity of Two Modules.
|g 1.
|t Reduction to the diagonal.
|g 2.
|t Completed tensor products.
|g 3.
|t Regular rings of equal characteristic.
|g 4.
|t Conjectures.
|g 5.
|t Regular rings of unequal characteristic (unramified case).
|g 6.
|t Arbitrary regular rings.
|g C.
|t Connection with Algebraic Geometry.
|g 1.
|t Tor-formula.
|g 2.
|t Cycles on a non-singular affine variety.
|g 3.
|t Basic formulae.
|g 4.
|t Proof of theorem 1.
|g 5.
|t Rationality of intersections.
|
| 650 |
|
0 |
|a Geometry, Algebraic.
|0 http://id.loc.gov/authorities/subjects/sh85054140
|
| 650 |
|
0 |
|a Local rings.
|0 http://id.loc.gov/authorities/subjects/sh85077942
|
| 650 |
|
0 |
|a Modules (Algebra)
|0 http://id.loc.gov/authorities/subjects/sh85086470
|
| 650 |
|
0 |
|a Dimension theory (Algebra)
|0 http://id.loc.gov/authorities/subjects/sh85038034
|
| 650 |
|
7 |
|a Dimension theory (Algebra)
|2 fast
|0 http://id.worldcat.org/fast/fst00893847
|
| 650 |
|
7 |
|a Geometry, Algebraic.
|2 fast
|0 http://id.worldcat.org/fast/fst00940902
|
| 650 |
|
7 |
|a Local rings.
|2 fast
|0 http://id.worldcat.org/fast/fst01001481
|
| 650 |
|
7 |
|a Modules (Algebra)
|2 fast
|0 http://id.worldcat.org/fast/fst01024523
|
| 700 |
1 |
|
|a Chin, CheeWhye.
|
| 901 |
|
|
|a ToCBNA
|
| 903 |
|
|
|a HeVa
|
| 035 |
|
|
|a (OCoLC)44084015
|
| 929 |
|
|
|a cat
|
| 999 |
f |
f |
|i e528f818-a24e-54bc-9034-236c5cd4f190
|s 2bcdc3e6-6762-5e48-8ee2-0a4164e93854
|
| 928 |
|
|
|t Library of Congress classification
|a QA564 .S4313 2000
|l Eck
|c Eck-Eck
|i 4591944
|
| 927 |
|
|
|t Library of Congress classification
|a QA564 .S4313 2000
|l Eck
|c Eck-Eck
|e MAYB
|b 56336495
|i 6897598
|
