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| Glaz S. — Commutative Coherent Rings |
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| Предметный указатель |
 -Lemma 172
(zero) Cohomology of an ideal,  165
Alfonsi’s Reduction Theorem 254
Algebra exterior power,  78
Algebra finitely presented 40
Algebra symmetric, S(M) 307
Algebra tensor, T(M) 78
Algebra, T-algebra 118
Algebraically compact,  281
Alternating matrix 198 199
Ascend 108
Associated primes, Ass(M) 85
Augmentation ideal 295
Augmentation map 295
Augmentation of an element 295
Basis (of a free module) 1
Buchsbaum — Eisenbud exactness criteria 250
cartesian 15
Cartesian “general format” 150
Cocartesian square 16
Completion 191
Complex M. 101
Complex M. deleted,  229
Complex M. homology (of complex), H(M),  101
Complex M. Koszul, K.(f,M) 102 103
Complex M. tensor product (of complexes) 102
Content of a polynomial c(f) 226
Content of an ideal c(I) 226
D+M construction 159
Depth (of a module), depth M 248
Descend 108
Differentiation 101
Dimension finitistic projective (of a ring), FP dim 61
Dimension global (of a ring), gl.dim 19
Dimension infective (of a module), inj.dim 18
Dimension Ng (of a module) 221
Dimension Ng (of a ring) 221
Dimension projective (of a module), proj.dim 17
Dimension pure (of a module), pure dim 63
Dimension pure (of a ring) 65
Dimension small finitistic projective (of a module), fP dim M, 244
Dimension small finitistic projective (of a ring), fP dim 61
Dimension weak (of a module), w.dim M 19
Dimension weak (of a ring), w.dim 20
Divisor (of a module), d(M) 205
Domain Bezout 25
Domain Dedekind 27
Domain finite conductor 160
Domain G.C.D. 207
Domain G.D. 172
Domain G.U. 172
Domain L.O. 172
Domain Prufer 24
Domain unique factorization 207
Domain valuation 23
Duality homomorphism 5
Envelope infective, E(M) 5
Epimorphism flat 13
Euler characteristic, X(M) 99
Extension ring 108
Extension, essential 5
Extension, flat epimorphic 13
Extension, ideally closed 282
Extension, maximal flat epimorphic, M(R) 130
Extension, trivial,  139
Fitting invariant (ideal),  96
Going down 172
Going up 172
Grade,  230 243
Grade, local,  251
Height 204
Hilbert Syzygies Theorem 23
Ideal, almost complete intersection 198
Ideal, augmentation 295
Ideal, conductor 174
Ideal, divisorial 204
Ideal, fractionary 204
Ideal, inverse (of an),  24 204
Ideal, invertible 24 204
Ideal, perfect 198
Ideal, T—nilpotent 61
Incomparable 172
Integral closure 170
Irreducible components 74
Isolated subgroup 24
Jensen‘s Lemma 22
Krull Akizuki Theorem 170
Lattice 29
Lying over 171
Macauley example 195
Map augmentation, aug 295
Map chain 101
Map homotopic 229
Map homotopic over A 229
Map homotopic over f 229
Map null homotopic 228
Map uniformity 191
McCoy Theorem 211
Module, absolutely pure 282
Module, absolutely pure 13
Module, coherent 41
Module, countably presented 282
Module, divisible 4
Module, faithful 112
Module, faithfully flat 9
Module, finitely presented 31
Module, flat 7
| Module, free 1
Module, infective 3
Module, projective 1
Module, semisimple 26
Module, simple 25
Module, uniformly coherent 191
Module, universal infective 6
Mori Nagata Theorem 170
Nagata‘s Theorem 170
Overring proper 171
Pair coherent 182
Pair G.D. 183
Pair G.U. 183
Pair INC. 183
Pair L.O. 183
Pair module finite 183
Pair Noetherian 182
Pair normal 182
Pair normal of rings 182
Pfaffian 198
Pointwise inverse (of an element)  137
Pointwise invertible element (unit) 137
Presentation finite 32
Presentation, finite n-presentation 32
Presentation, n-presentation 31
Rank of a flat module 85
Rank of a free module 77
Rank of a module over a domain 84
Rank of a projective module 77
Rank of a valuation 24
Rank of an abelian group 84
Rees ring, R(I) 265
Resolution, finite 2
Resolution, free 2
Resolution, infective 4
Resolution, projective 2
retract 111
Retraction (map) 111
Ring, algebraically compact 281
Ring, self-injective 282
Ring, absolutely flat (Von Neumann regular) 27
Ring, boolean 28
Ring, coherent 44
Ring, complete boolean 292
Ring, completely integrally closed 24
Ring, countably complete boolean 292
Ring, divided 172
Ring, Gorenstein 148
Ring, group 294
Ring, hereditary 27
Ring, polynomial 228
Ring, power series 280
Ring, reduced 87
Ring, regular 200
Ring, regular, of continuous functions 321
Ring, regular, of global dim 2 212
Ring, regular, of weak dim 2 219
Ring, self-associated 92
Ring, self-injective 123
Ring, semihereditary 26
Ring, semisimple 26
Ring, stably coherent ring 255
Ring, super regular 210
Ring, total of quotients 112
Ring, unibranched 172
Ring, uniformly coherent 191
Ring, universal absolutely flat 137
Schanuel‘s Lemma 3
Sequence, regular 235
Sets, completely separated 322
Sets, cozero (of a function) 322
Sets, disjoint 282
Sets, negative (of a function) 322
Sets, orthogonal 282
Sets, positive (of a function) 322
Sets, zero (of a function) 322
Socle 200
Space completely regular 322
Space connected 74
Space Hausdorff 74
Space Noetherian 74
Space,  74
Space, basically disconnected 322
Space, P-space 327
Spectrum (of a ring), Spec(R) 73
Spectrum (of a ring), Spec(R), maximal, Max(R) 219
Spectrum (of a ring), Spec(R), minimal, Min(R) 86
Submodule pure 281
Submodule pure 11
Support of a module, Supp(M) 95
Support of an element 294
Support subgroup 294
System of linear equations (countable) 281
System of parameters (regular) 319
Total ring of quotients, Q(R) 112
Trace (of a module),  83
Unique divisibility 301
Upper of zero 265
Urysohn‘s Extension Theorem 323
Valuation 24
Valuation discrete 23
Valuation domain 23
Valuation rank of a 24
Value group 24
Wedderburn theorem 26
Zariski topology 73
Zariski topology locally (for the Zariski topology) 75
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