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| Villareal R.H. — Monomial algebras |
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| Предметный указатель |
Normalization of an edge subring 320
Normalization of monomial subrings 218
Normalized degree 203
Normalized grading 265
Normalized volume 228
Normally torsion free 77
Normally torsion free, edge ideal 312
Normally torsion free, versus normal 79 238
Nullstellensatz 46
Numerical semigroup 377
Odd cycle condition 322
Order complex 170
Partition 150
Pascal identity 15
Path 162
Perfect matching 165
Polarization 131
Polarization of a bipartite planar graph 304
Polarization of an even closed walk 304
Polyhedral cone 210
Polyhedral set 210
Polyhedral set, face 211
Polyhedral set, facet 214
Polynomial, function 15
Polynomial, quasi-homogeneous 13
Polytopal subring 228
Polytope 154
Polytope, lattice 228
PORTA 211
POSET 169
Positively graded algebra 35
Presentation of a graded algebra 35
Presentation, ideal 35 66 202
Primary decomposition of a graded module 14
Primary decomposition of a module 7
Primary decomposition of an ideal 7
Primary decomposition of monomial ideals 132
Primary decomposition, irredundant 7
Primary ideal 6
Primary ideal, extension of 27
Primary submodule 6
Prime avoidance, general version 10
Prime avoidance, graded version 41
Primitive binomial 284
Projective closure 57
Projective closure of a monomial curve 375
Projective dimension 61
Projective space 56
Proper face of a polyhedral set 211
Proper face of a polytope 155
Pure resolution 62
Pure simplicial complex 145
Quasi-regular sequence 83
Radical ideal 76
Radical of an ideal 4
Rank of a module 10
Reduced ring 4
Reduced simplicial homology 139
Reduction number of an algebra 349
Reduction number of an ideal 339
Reduction of a polynomial 49
Rees algebra 66
Rees algebra of a filtration 81
Regular element 6
Regular ring 19
Regular ring is Cohen — Macaulay 89
Regular sequence 16
Reisner Theorem 143
Relative interior 215
Remainder 49
Residue field 2
Revlex order 48
Ring extension 23
S-polynomial 49
Samuel function 85
Saturated graph 177
Saturation of an ideal 53
Segre product 105
Segre variety 414
Semigroup 377
Semigroup, ring 201 367
Serre's normality criterion 26
Set of k-products 256
Shellable complex 146
Shelling 146
Shift in the graduation 59
Simple components 368
Simple module 9
Simplex in affine space 155
Simplex of a simplicial complex 138
Simplex, lattice 228
| Simplex, oriented 139
Simplex, unimodular 228
Simplicial complex 138
Simplicial complex, Alexander dual 198
Simplicial complex, Cohen — Macaulay 143
Simplicial complex, geometric realization 156
Simplicial polytope 155
Simplicial sphere 156
Simplicial sphere, Gorenstein property 157
Skeleton of a complex 145
Sliding depth 29
Socle of a graded algebra 111
Socle of a module 21
Spanning subgraph 162
Spectrum of a ring 2
Square 163
Square-free monomial 130
Standard algebra 35
Standard grading 13
Stanley — Reisner complex 142
Stanley — Reisner ideal 142
Stanley — Reisner ring 142
Star 187
Star of a face 148
Strongly Cohen — Macaulay 29
Subgraph 162
Subring of k-products 203
Support of a binomial 387
Support of a module 5
Support of a monomial 131 299
Support of a vector 296
Supporting hyperplane 211
Suspension of a graph 325
Symbolic power 76
Symbolic Rees algebra 238
Symmetric algebra 65 67
Symmetric semigroup 378
System of parameters 19
System of parameters for modules 16
System of parameters, homogeneous 36
Syzygetic ideal 67
Syzygy module 51 61
Syzygy module, computation of 52
Tensor algebra 65
Term order 48
Terminal cycle 316
Terms 48
Toric ideal 202 404
Toric ideal of an edge subring 282
Toric set 403
Toric variety 208
Total ring of fractions 8
Transcendence basis 34
Transcendence degree 34
TREE 163
triangle 163
Triangulated graph 194
Twists of a graded module 61
TYPE 266
Type of a module 21
Type, Cohen — Macaulay 112
Unicyclic graph 316
Unimodular covering 230
Unimodular matrix 295
Unimodular matrix, totally 414
Unmixed graph 168
Unmixed ideal 20
Upper bound conjecture 159
Usual grading 13
Valuation ring 378
Variety, affine 45
Variety, coordinate ring 45
Variety, dimension of 45
Variety, irreducible 45
Variety, irreducible components 46
Variety, projective 56
Variety, toric 208
Veronese subring 203
Veronese subring, square-free 203
Veronese variety 412
Vertex 212
Vertex cover 165
Vertex cover, minimal 165
Vertex covering number 165
Vertex critical graph 168
Walk 162
Walk, closed 162
Zariski closure 207
Zariski topology 45
Zariski topology of the prime spectrum 2
Zero divisor 6
Zero set of an ideal 45
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