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Boffi G., Buchsbaum D. — Threading Homology through Algebra: Selected Patterns
Boffi G., Buchsbaum D. — Threading Homology through Algebra: Selected Patterns



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Название: Threading Homology through Algebra: Selected Patterns

Авторы: Boffi G., Buchsbaum D.

Аннотация:

Threading Homology through Algebra takes homological themes (Koszul complexes and their variations, resolutions in general) and shows how these affect the perception of certain problems in selected parts of algebra, as well as their success in solving a number of them. The text deals with regular local rings, depth-sensitive complexes, finite free resolutions, letter-place algebra, Schur and Weyl modules, Weyl-Schur complexes and determinantal ideals. Aimed at graduates and academics in mathematics, the book provides an overview of the developments that have taken place in these areas as well as an insight into some of the open problems which exist.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 255

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Rel(\lambda/ \mu)$ (almost skew-shape)      171
$Rel(\lambda/ \mu)$ (skew-shape)      170
$Tor_n$      18
$t^+$-complex      215
$t^+$-graded strand      215
$t^+$-submodule      215
Acyclic complex      70
Acyclicity Lemma      107
Almost partition      152
Almost skew-partition (-shape)      150
Alternating map      128
Artin — Rees theorem      48
Associate      1
Associated prime ideal      50
Associator of a module      50
Bar algebra      213
Bar complex      80
Bar shape      150
Betti numbers      144 209
Canonical basis      9
Capelli Identities      166 167
Cocommutative graded R-coalgebra      27
Codimension of a module      52
Cohen — Macaulay module      63
Cohen — Macaulay ring      63
Cohen — Macaulay Theorem      55
Column word of a tableau      178
Column-convex shape matrix      150
Column-standard      175
Commutative graded R-algebra      27
COMPLEX      13
Connected graded algebra      215
Content of a tableau      206
Coprime      2
Cyclic module      69
Dedekind domain      4
Depth of a module      52
Diagonal map      26
Differential bar complex      212
Dimension of a ring      47
Dimension of an R-module      47
Discrete valuation ring      6
Divided power algebra      28
Divisor      1
Dual basis      28
Durfee square      144 201
Equicharacteristic      65
Euclidean Domain      7
Exact complex      13
Extension      21
Exterior algebra      30
Extn      20
Extreme flippable inversion      178
Factorization domain      2
Finite free module      10
Finitely presented      13
Finitistic global dimension      53
First difference function      46
First Structure Theorem      110
Flippable inversion      175
Free bar module      214
Free dimension      18
Free module      9
Free presentation      13
Free resolution      17
Generic (universal) resolution      144
Generic alternating map      137
Global dimension      44
Gorenstein ideal      127
Grade of an ideal      127
Graded R-algebra      23
Greatest common divisor      1
Height of a module      50
Height of a prime ideal      48
Hereditary ring      16
Hilbert basis theorem      7
Hilbert — Burch theorem      111
Homogeneous element      23
Homogeneous strands $Z_{n,m}^{(\xi)} \odot \underline{Z}_{n,m}^{(l)}$      221
Homological conjectures (list of)      66
Homological dimension      3 17
Homology functor      94
Hopf algebra      26
Ideal of definition      48
Integral weight      205
Intersection multiplicity      64
Intertwining numbers      207
inversion      175
Irreducible element      2
Jacobi — Trudi matrix      228
Koszul complex      39
Krull Principal Ideal Theorem      50
Last row (column) of shape matrix      149
Least common multiple      1
Length of a partition      151
Length of a skew-shape      151
Length of almost skew-shape      152
Letter-place superalgebra      164
letters      158
Lifting problem      112
m-sequence      42
Mapping cone      39
Mapping cone construction      39
Maximal spectrum of R      5
Measuring identity      88
Minimal resolution      53 144
Mixed characteristic      66
Modified column word of a tableau      178
Multi-signed alphabet      175
Multiplicity of M with respect to E      101
Multiplicity of q with respect to E      60
Multiplicity of R      60
Multipliers      111
n-th extension module      20
n-th torsion module      18
Nakayama's lemma      15
Noetherian      3
Noetherian ring      4
Normalized bar complex      80
Operators $Z_{i,j}^{(k)}$      215
Oriented free module      110
Parameter matrix for a module      101
Partition      150
Perfect ideal      52
Pfaffian      129
Pfaffian ideal      130
Place polarization      165—167
Places      158
Polynomial      6
Polynomial function      46
Power series (formal)      6
Prime element      2
Projective dimension      3
Projective module      14
Projective resolution      17
Proper divisor      1
Quillen — Suslin theorem      15 114
R-algebra      22
R-coalgebra      24
R-maps      9
Rank of a free module      10
Rank of a map      104
Rank of a projective module      104
Regular local ring      54
Regular sequence      42
Reversed column word of a tableau      178
Rigidity problem      108
Robinson — Schensted — Knuth (R–S–K)      241
Row tableau      153
Row-convex shape matrix      150
Row-standard tableau      158 175
Samuel multiplicity      60
Saturated chain condition      55
Saturated chain of prime ideals      55
Schur algebra      204
Schur complexes      197
Schur map      155 169
Schur modules (general)      155
Schur modules (hooks)      80
Second Structure Theorem      122
Separators      213
Shape matrix      149
Short exact sequence      13
Signed inequalities      175 176 186
Skew-partition (-shape)      150
Spectrum of R      5
Split exact sequence      13
Standard double tableau      159 162 164
Standard tableau      175
Standard tableau (for hooks)      79
Straight filling      182
Straight tableau      175
Subshape      150
Symmetric algebra      23
Symmetrization      28
System of divided powers      129
System of parameters      48
T-boundary operator      213 214
T-grading      213
t-hook      225
Tableau with values in S      153
Taylor algorithm      182
Tensor algebra      24
Tensor product      15
Torsion element      18
Torsion module      18
Torsion submodule      18
Torsion-free      18
Transpose (dual) of a shape      152
Trivial extension      21
Type of almost skew-shape      152 170
Unflippable inversion      175
Unique factorization domain (UFD)      2 59 111
Universal Coeficient Theorem      206
Universal freeness      73
Unmixed ideal      56
Weight of a shape      153
Weight submodule      205
Weyl map      154 169
Weyl modules (general)      155
Weyl modules (hooks)      80
Weyl — Schur complex      190
Weyl — Schur map      190
Z-forms      203
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