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Bruns W., Vetter U. — Determinantal Rings
Bruns W., Vetter U. — Determinantal Rings



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Название: Determinantal Rings

Авторы: Bruns W., Vetter U.

Язык: en

Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 236

Добавлена в каталог: 27.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute invariant      74 86
Absolute semi-invariant      76
Acyclicity criterion      207 208
Algebra generated by the t-minors      132 133 151
Algebra with straightening law (ASL)      38
Algebraic quotient      80
Analytic spread      117
Arithmetical rank      61
Arithmetical rank of a determinantal ideal      62 81
Arithmetical rank of an ideal dening a Schubert cycle      62
Arithmetical rank of an ideal generated by a poset ideal      62
Arithmetical rank of an ideal generated by a poset ideal, in a symmetric ASL      62
ASL      38
ASL, discrete      62
ASL, symmetric      43
ASL-property of a determinantal ring      52
ASL-property of a graded ring derived from a straightening-closed ideal      108 110
ASL-property of a Schubert cycle      53
ASL-property of B[X] on $\Delta(X)$      48
ASL-property of G(X) on $\Gamma(X)$      41
Associated graded module      30
Associated graded ring      30 108
Associated graded ring derived from a straightening-closed ideal      109
Associated graded ring derived from an ideal of maximal minors      112 114
Associated graded ring derived from the ideal of t-minors      132
Associated prime ideals      1
Associated prime ideals of a G-stable ideal      148 149
Associated prime ideals of powers of a determinantal ideal      132
Auslander — Bridger dual      214
Auslander — Buchsbaum equation      1
Auslander-module      198
Auslander-module and rigidity      199 200
Bitableau      138
Bitableau, left (right) final      139
Bitableau, left (right) initial      139
Bitableau, standard      138
Canonical (divisor) class      93
Canonical (divisor) class of a determinantal ring      97 98 103
Canonical (divisor) class of a Schubert cycle      97 102
Canonical module      210
Canonical module of a determinantal ring      22 97 98 103 115
Canonical module of a Schubert cycle      97 102 115
Class group      see Divisor class group
Cofactors, matrix of      3
Cohen — Macaulay module      209
Cohen — Macaulay property and perfection      210
Cohen — Macaulay property of a determinantal ring      13 25 60
Cohen — Macaulay property of a graded ring derived from an ideal of maximal minors      112
Cohen — Macaulay property of a Schubert cycle      60
Cohen — Macaulay property of an ASL      59
Cohen — Macaulay ring      209
Cohen — Macaulay type of a determinantal ring      115
Complete intersection      198
Content of a tableau (bitableau)      138
D-ideal      145
D-ideal, primary      147
D-ideal, prime      147
D-ideal, principal      146
D-ideal, radical      147
Decomposition of K[X] into irreducible G-modules      143 144
Dehomogenization      211
Dehomogenization and being reduced      212
Dehomogenization of a homogeneous ideal      212 213
Dehomogenization, B[X] as a      48
Dehomogenization, integrity      212
Dehomogenization, normality      212
Dening ideal of an ASL      40
Dening ideal of G(X)      43
Depth      see also Grade
Depth of a module      1 206
Derivations, almost perfection      188
Derivations, module of      184
Derivations, perfection      192
Derivations, system of generators      188
Derivations, syzygetic behaviour      197
Derivations, syzygies      189
Determinantal ideal      5 51 155 156 175
Determinantal ideal of a homomorphism      202
Determinantal ring      4 5
Determinantal ring as a      53
Determinantal ring as a ring of absolute invariants      76 86 87 160
Determinantal variety      4 6
Diagram      136
Differentials, depth      180 181 183
Differentials, free locus      178
Differentials, grade      180 183
Differentials, module of      174
Differentials, presentation as a second syzygy      186
Differentials, syzygetic behaviour      182
Differentials, syzygies      181
Dimension of a determinantal ring      57
Dimension of a Schubert cycle      57
Dimension of an ASL      55
Discrete ASL      62
Divisor class group of a determinantal ring      95 96 160
Divisor class group of a Schubert cycle      95
Dual basis      2
Dual of a homomorphism      2
Dual of a module      2
Dualizing module      210
Eagon — Northcott complex      16
Extended Rees algebra      108
Extended Rees algebra derived from a straightening-closed ideal      108 109
Extended Rees algebra derived from an ideal of maximal minors      112 114
Extended symbolic Rees ring      124
Extended symbolic Rees ring derived from a determinantal ideal      124
Extraspecial pair      43
Factoriality of a determinantal ring      95
Factoriality of a Schubert cycle      69 95
Fitting invariants of a module      203
Form ideal, form module      30
Free resolution      18 21
Free resolution of a generic module      172
Free resolution of an ideal, of maximal minors      18
Free resolution of an ideal, submaximal minors in a quadratic matrix      25
Free resolution of symmetric and exterior powers      18 21
Free resolution of the image of a generic map      172
Full semigroup      150
G-decomposition of K[X]      143 144
G-module      80
G-stable ideals of K[X]      146
G-submodule generated by a bitableau      145
Generic map      162
Generic map, free resolution of the image      172
Generic map, perfection of the image      164 165
Generic module      162
Generic module, almost perfection      164
Generic module, free resolution      172
Generic module, perfection      18 167 170
Generic module, projective dimension      171
Generic module, reflexivity      162
Generic module, syzygetic behaviour      171 172
Generic perfection      27
Generic perfection and substitution of indeterminates      31 32
Generic perfection of a determinantal ideal      61
Generic perfection of a Schubert cycle      61
Generic perfection of the canonical module      30
Generic point      73
Generic point of a determinantal ring      74 85 87
Generic point of a Schubert cycle      83 85
Generically perfect ideal      27
Generically perfect module      27
Gorenstein property      210
Gorenstein property of a determinantal ring      22 25 98 104
Gorenstein property of a Schubert cycle      102
Gorenstein ring      210
Grade      206
Grade and projective dimension      207
Grade estimates for modules of invariants      89
Grade estimates for powers of ideals of maximals minors      90 118 119
Grade estimates for symbolic powers of a determinantal ideal      125
Grade of a determinantal ideal      12 61 159
Grade of a module      206
Grade of an ideal      206
Grade of an ideal dening a Schubert cycle      61
Grade, behaviour along exact sequences      207
Grade, homological description      206
Grade, local description      207
Grassmann variety      6 8
Gulliksen — Negard complex      22
Height of a determinantal ideal      12 61 159 175
Height of a specialization of a perfect ideal      36
Height of an ideal dening a Schubert cycle      61
Height of an ideal generated by minors of a matrix      10 11
Hilbert — Burch theorem      218
Homogenization of an ideal      212 213
Ideal in a partially ordered set      50
Ideal in a partially ordered set, cogenerated by a subset      51
Ideal in a partially ordered set, generated by a subset      51
Ideals of maximal minors      10 105
Ideals of maximal minors, free resolution      18
Indecomposability ob the subspace of (right) initial bitableaux      142
Induction argument for determinantal rings      see Localization argument
Integral closure of a G-stable ideal      149
Integrity of a determinantal ring      14 65 158
Integrity of a graded ring derived from an ideal of maximal minors      114
Integrity of a Schubert cycle      65
Invariant      80
Invariant, absolute      74 86
Invariant, theory, main problems      80
Invariant, versus absolutely invariant      75
Isotopic component      142
Kaehler differentials      see Differentials
Koszul complex      17
Leading form      30 108
Linear independence of standard monomials in G(X)      43 84
Linearly reductive      80 81
Localization argument for determinantal rings      11 66 122
Localization argument for Schubert cycles      64
Locally upper semi-modular poset      58
Maximal minors      3 105
Maximal minors, ideals of      10 105
Maximal minors, powers of ideals of      106 114
Maximal minors, subalgebra of      106 107 112
Minimal primes of an ideal generated by a poset ideal, in $\Delta(X)$      66
Minimal primes of an ideal generated by a poset ideal, in $\Gamma(X)$      66
Minor of a matrix      3
Module of derivations      see Derivations
Module of differentials      see Differentials
Module, n-th syzygy      214
Module, n-torsionfree      213
Module, n-torsionless      214
Module, reflexive      214
Module, torsionfree      213
Multiplicity of a (maximal minors) determinantal ring      16
Normal subsemigroup      150
Normality criterion      212
Normality of a determinantal ring      15 61 65 150 160
Normality of a graded ring derived from an ideal generated by maximal minors      114
Normality of a Schubert cycle      65
Perfect ideal      209
Perfect module      209
Perfection      209
Perfection and Cohen — Macaulay property      210
Perfection of a determinantal ideal      13 18 25 61 159 175
Perfection of a Schubert cycle      61
Perfection of a specialization      28 29
Pluecker coordinates      6
Pluecker map      6
Pluecker relations      41
POSET      39
Powers of an ideal generated by a regular sequence      15 29
Powers of an ideal of maximal minors      79 114
Powers of determinantal ideals      79 114 130 149
Primary decomposition of a G-stable ideal      148 149
Primary decomposition of products of determinantal ideals      126 130 149
Prime elements in a determinantal ring      97
Principal radical system      155
Principal radical system of determinantal ideals      158
Products of determinantal ideals      126 137
Radical of a D-ideal      147
Radical subsemigroup      150
Rank of a free module      1
Rank of a module      1 204
Rank of a poset element      55
Rank of a subset of a poset      55
Rational representation      80
Rational singularity      81 150
Reduced ASL      54
Reduced determinantal ring      15 55
Reduced Rees algebra      108
Reduced Rees algebra, derived from a straightening-closed ideal      110 111
Reduced Rees algebra, derived from an ideal of maximal minors      112 114
Reduced Rees algebra, extended      108
Reduced ring      1
Reduced Schubert cycle      55
Reflexive module      214
Regular elements in an ASL      55 56
Reynolds operator      81 88
Rigidity      198 200
Ring of invariants, being noetherian      81
Ring of invariants, Cohen — Macaulay property      81
Ring of invariants, existence of a Reynolds operator      81
Ring of invariants, normality      81 115 149
Ring of invariants, rational singularities      81 149
Ring of U-invariants      149
Ring of U-invariants in a determinantal ring      150
Schubert cycle      6 9
Schubert cycle as a ring of absolute invariants      76 86
Schubert variety      6 8
Segre product of ASLs      107
Self-covering poset ideal      110
Serre type criterion for torsionfree modules      213
Serre's condition ($R_2$) for a determinantal ring      71
Serre's condition ($R_2$) for a Schubert cycle      71
Serre's condition ($S_n$) for an ASL      60
Shape of a monomial      135
Singular locus of a determinantal ring      12 70 71 160
Singular locus of a Schubert cycle      68
Special pair      43
Spectrum of a ring      1
Standard basis      38
Standard bitableau      138
Standard monomial      38
Standard monomials as generators of an ASL      39
Standard representation      39
Standard representation of a bitableau      138 139
Standard representation of a monomial      39
Standard tableau      138
Straightening law      38
Straightening relations      38
Straightening-closed ideal      108
Straightening-closed ideal, extended Rees-algebra derived from a      108
Straightening-closed ideal, powers of a      108
Submaximal minor      3
Support of a module      1
Support of a monomial      131
Symbolic graded ring      124
Symbolic graded ring, derived from a determinantal ideal      124
Symbolic powers of determinantal ideals      122 123 124 126 129 130 149
Symbolic powers of determinantal ideals, intersection of      136 137
Symmetric algebra of a straightening-closed ideal      111
Symmetric ASL      43
Syzygies of a generic module      166
Syzygies of an ideal generated by a poset ideal      53
Syzygies of determinantal ideals      164 175
Syzygy module      214
Tableau      137
Tableau, final      139
Tableau, initial      139
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