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| Villareal R.H. — Monomial algebras |
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| Предметный указатель |
a-invariant 99
Adjacency matrix 190
Admissible grading 220
Affine combination 210
Affine k-algebra 31
Affine space 45 210
Affine space, generated by a set 210
Algebra 23
Algebra of finite type 23
Algebra, finite 23
Algebra, finitely generated 23
Almost integral 74
Annihilator 4
Arithmetical rank 414
Artin — Rees lemma 85
Artinian, reduction 123
Artinian, ring 10
Ascending chain condition 2
Associated graded algebra 73
Associated matrix of a monomial subring 202
Associated prime of a module 5
Associated prime of an ideal 5
Atomic cycles 303
Betti numbers 61
Betti numbers, initial 188
Betti numbers, initial virtual 188
binomial 202
Binomial of a closed walk 282
Binomial, expansion 100 119
Binomial, ideal 202
Bipartite graph 163
Boundary complex 156
Bow tie 317
Buchberger algorithm 50
Buchberger criterion 51
Canonical module 106
Catenary ring 21
Cayley — Hamilton 22
Ceiling of a vector 234
Characteristic of a ring 2
Chinese remainder theorem 10
Chord of a cycle 194
Chordal graph 194
Circuit 297
Circuit of a graph 300
CoCoa see "Computer algebra" 94
Codimension of a module 4
Codimension of an ideal 4
Cohen — Macaulay graph 168
Cohen — Macaulay ideal 20
Cohen — Macaulay module 18
Cohen — Macaulay ring 20
Complement of a graph 175
Complementary complex 172
Complete bipartite graph 182
Complete generically 68
Complete graph 163
Complete ideal 69
Complete intersection 20
Complete set theoretic 20
Composition series 9
Computer algebra systems, CoCoA 94
Computer algebra systems, Macaulay 53
Computer algebra systems, Normaliz 236
Computer algebra systems, PORTA 211
Cone 210
Cone of a complex 140
Cone over a graph 293
Cone, finitely generated 211
Conormal module 67
Content of a polynomial 339
Convex, combination 154 210
Convex, cone 210
Convex, hull 154 210
Convex, polyhedron 210
Convex, set 210
Cover complexity 166
Critical binomials 385
Critical binomials, full set 385
Cutpoint 175
CYCLE 163
Cycle, basis 291
Cycle, space 291
Cyclic polytope 158
D-tree 194
Danilov — Stanley formula 221
Dedekind — Mertens formula 339
Degree of a module 101
Degree of a vertex 162
Dehn — Sommerville equations 157
Depth of a module 18
Depth, lemma 18
Dickson's lemma 48
Dimension of a set 210
Dimension of a simplicial complex 138
Dimension, theorem 16
Discrete graph 162
Discrete valuation 378
Distance 163
Division algorithm 49
Dominant set 175
Duality in monomial subrings 268
Duality in Stanley— Reisner ideals 196
EDGE 161
Edge, cone 326
Edge, critical graph 168
Edge, generator 282
Edge, graph 188
Edge, ideal 168
Edge, ideal, generalized 256
Edge, subring 282
Ehrhart, polynomial 232
Ehrhart, polynomial, normalized 227
Ehrhart, ring 232
Ehrhart, ring, normalized 226
Elementary integral vector 297
Elementary vector 296
Elementary zonotope 302
Elimination order 52
Embedded prime 10
End vertex 162
Equations of a cone 216
Euler characteristic 141
Euler characteristic, reduced 141
Euler formula 156
Even cycle 163
Exact sequence 5
Exact sequence, short 5
Extended Rees algebra 72
Extremal Cohen — Macaulay ring 117
Extremal Gorenstein ring 115
f-vector of a complex 150
f-vector of a polytope 155
Face 138 211
Face, ideal 130
Face, ring 143
Facets of a cone 325
Facets of a simplicial complex 144
Faithfully flat 27
Farkas's lemma 218
Field of fractions 8
Filtration of a ring 81
Finite homomorphism 23
Finite length 9
Flag complexes 170
Flat homomorphism 27
Forest 163
Forms 13
Frobenius Number 378
Gauss lemma 339
| Geometrically linked 30
Going down 26
Going up 26
Gorenstein graded ideal 112
Gorenstein ideal 22
Gorenstein ring 22
Graded algebra 16
Graded ideal 13
Graded map 13
Graded module 13
Graded ring 12
Graph 161
Graph, connected 162
Graph, connected components 162
Graver basis 284
Groebner basis 49
Groebner basis of toric ideals 203
Groebner basis, lexicographical 276
Groebner basis, reduced 49
H-configuration 314
h-vector of a C-M complex 152
h-vector of a complex 152
h-vector of a polytope 156
h-vector of a standard algebra 108
Height of an ideal 4
Herzog — Kuehl formulas 63
Hilbert basis theorem 2
Hilbert function 14 97
Hilbert polynomial 101
Hilbert polynomial of a face ring 150
Hilbert polynomial over an Artinian ring 15
Hilbert series 97
Hilbert series of a face ring 150
Hilbert — Burch theorem 62
Hochster configuration 314
Homogeneous element 13
Homogeneous ideal 13
Homogeneous resolution 61
Homogeneous ring 14
Homogeneous subring 224
Homogenization of an ideal 54
Homomorphism of algebras 23
Homomorphism of rings 2
Homomorphism, integral 23
Ideal of a subset 45
Ideal of linear type 67
Ideal of relations 35
Ideal, quotient 4
Improper face of a polyhedral set 211
Incidence matrix 294
Incidence matrix, Smith form 295
Independence number 165
Independent set of edges 163
Independent set of vertices 165
Induced subgraph 195
Initial degree 110
Initial ideal 48
Integral closure 23
Integral closure of a domain 26
Integral closure of an edge subring 320
Integral closure of ideals 69
Integral closure of monomial ideals 234
Integral closure of monomial subrings 218
Integral closure, commute with localizations 70 71
Integral extension 23
Integrally closed ideal 69
Integrally closed ring 26
Irreducible representation 214
Irreducible representation of a cone 215
Irreducible submodule 6
Irredundant decomposition of modules 7
Irrelevant maximal ideal 35
Isolated prime 10
Isolated vertex 162
Jacobian criterion 91
Jacobian ideal 92
Jacobian matrix 91
Jacobson radical 95
Join of graphs 332
Join of ideals 245
Join of simplicial complexes 140
Koenig Theorem 165
Koszul complex 28
Krull dimension 4
Krull intersection theorem 83
Krull Principal Ideal Theorem 19
Kruskal — Katona criterion 151
Lattice 135
Lattice of monomial ideals 135
Lattice, distributive 135
Laurent polynomials 80
Leading coefficient 48
Leading monomial 48
Leading term 48
Length of a module 9
Level algebra 274
Lex order 31 48
Linear resolution 63
Linear variety 210
Link of a face 143
Linkage class 30
Linkage class, even 30
Linkage of ideals 30
Local ring 2
localization 3
Localization at a prime 3
Locally a complete intersection 78
Log set 236
Macaulay see "Computer algebra" 53
Macaulay, symbol 119
Macaulay, theorem 119
Marriage problem 165
Marriage problem, a generalization 330 331
Minimal primes of a module 9
Minimal primes of a ring 2
Minimal resolution 61
Minimum number of gens 58
Module of finite length 9
Module of fractions 3
Monomial curve 367
Monomial ideal 130
Monomial ideal of minimal covers 196
Monomial ideal of mixed products 248
Monomial order 48
Monomial ring 130
Monomial subring 201
Monomial subring of a graph 282
Monomial walk 283
Multiplicity of a face ring 154
Multiplicity of a graded module 15 101
Multiplicity over a local ring 85
Nakayama's lemma, general version 8
Nakayama's lemma, graded version 14
Neighbor set of a subset 163
Neighbor set of a vertex 182
Neighbourly polytope 158
Nilpotent element 4
Nilradical 4
Noether normalization of a monomial ring 39
Noether normalization of an edge subring 309 340 362
Noether normalization, homogeneous 39
Noether normalization, lemma 34
Noetherian module 1
Noetherian ring 1
Normal ideal 69
Normal polytope 228
Normal ring 26
Normality, descent 80 240
Normaliz 236
Normalization of a ring 26
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