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Becker T., Weispfenning V. — Groebner bases and commutative algebra
Becker T., Weispfenning V. — Groebner bases and commutative algebra



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Название: Groebner bases and commutative algebra

Авторы: Becker T., Weispfenning V.

Аннотация:

The centerpiece of Grobner basis theory is the Buchberger algorithm, the importance of which is explained, as it spans mathematical theory and computational applications. This comprehensive treatment is useful as a text and as a reference for mathematicians and computer scientists and requires no prerequisites other than the mathematical maturity of an advanced undergraduate. Strong emphasis is placed on algorithms and their verification, with no sacrifices in mathematical rigor.


Язык: en

Рубрика: Математика/Алгебра/Вычислительная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 574

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$-compatible term order      466
$\Gamma$-degree      466
$\Gamma$-homogencous polynomial      466
$\Gamma$-homogeneous polynomial      466
$\sigma$-reduction      504
Abelima group      16
Abelima monoid      62
Abstract degree function      78
Additive monoid $\mathbb{N}^n$      62
Adequate reduction relation      178
Adjunction field      293
Adjunction ring      52
Admissible order      167
Algebraic closure      309
Algebraic element      293
Algebraic extension (field)      293
Algebraically closed field      306
Algebraically independent set      302
Algebraically independent set, maximal      303
Algorithm      9
Antisymmetric relation      150
Antomorphism      23
Associated prime ideal      352
Associated ring elements      38
Autoreduced      203
Axiom of Choice      141
Basis of a vector space      121
Basis of an algebra      434
Basis of an ideal      26
Basis, Dickson      159
Basis, minimal finite      161
Basis, w.r.t. a quasi-order      159
Bijection      7
Bijective      7
Binary operation      15
Binary relation      149
Block order      168 191
Block order, inverse      390
Boolean ring      283
Buchberger algorithm      213
Buchberger order      237
Buchberger triple      229
Buchberger's first criterion      222
Buchberger's Second Criterion      223
Canonical homomorphism      31
Cardinality      9
Cartesian product      5
Chain of prime ideals      323
Chain, strictly ascending      155
Chain, strictly descending      155
Characteristic      49
Chinese remainder theorem      115
Church — Rosser property      175
Coefficient      70 191
Coefficients of a linear equation      244
Coefficients of a polynomial      71
Comaximal      262
Combined structure constants      438
Commutative ring      19
Commutative toohold      62
Computable field      78 179
Computable K-vector space      126
Computable monoid      178
Computable PID      460
Computable ring      78 178
Computable UFD      111
Computable, Euclidean domain      78 179
Confluence      175
Confluence, local      175
Congruence relation      201
Congruent      32
Connex relation      150
Constant      69
Constant polynomial      69
CONT      389
Content      93
Contraction of an ideal      57
CONVGROEBNER      428
Coset      27
Critical pair      215
CRT      261
D-GROEBNER      460
D-Groebner basis      455
d-homogeneous part      474
D-reduction      453
Decidable order      179
Decidable reduction relation      178
Decidable set      178
Decomposition primary      362
Decomposition unmixed      399
Degree      71
Degree in a variable      74
Degree, F-degree      466
Degree, total      70 71
Dehomogenization      478
Depth      323
Derivative      101
Descending term      502
Diagonal      149
Dickson property      160
Dickson quasi-order      160
Dickson quasi-ordered set      162
Dickson's lemma      163 189
DIMENSION      449
Dimension of a vector space      130
Dimension of an algebra      434
Dimension of an ideal      271
Dimension of an ideal, strong      443
Direct product of quasi-ordered sets      163
Direct product of rings      53
Disjoint (terms)      222
Distance between intervals      414
Distance between point and interval      414
div      79
DIVINT      11
Divisibility      4 38
Divisibility relation      189
DIVPOL      81
Domain      20
Domain integral      20
Domain of a map      5
Domain principal ideal      41
Domain principal ideal, computable      460
Domain, Euclidean      78
Domain, Euclidean, computable      78 179
Domain, Euclidean, with unique remainders      463
Domain, unique factorization      90
Domain, unique factorization, computable      111
E-reduction      463
Elimination      258
Elimination ideal      256
Embedded primary component      363
Embedding of K-vector spaces      121
Embedding of monoids      63
Embedding of rings      23
Endomorphism      23
EQUIV      178
Equivalence class      152
Equivalence problem      173
Equivalence relation      150
Equivalence relation, associated with quasi-order      154
Euclidean algorithm      84
Euclidean algorithm, extended      4 84
Euclidean Domain      78
Euclidean domain with unique remainders      463
Exchange      132
EXPONENT      354
Exponent map      70 188
Exponent, univariate      345
EXTCONT      392
Extended Euclidean algorithm      4 84
Extension (field)      293
Extension (field), algebraic      293
Extension (field), finite      293
Extension (field), simple      293
Extension (field), transcendental      293
Extension of a relation      150
Extension of an ideal      57
Extension ring, finitely generated      52
EXTEUC      83
EXTGROEBNER      239
EXTREDGROEBNER      240
Factor module      136
Fermat's theorem      51
Field      20
Field extension      293
Field extension, algebraic      293
Field extension, finite      293
Field extension, simple      293
Field extension, transcendental      293
Field of fractions      55
Field of quotients      55
Field quotient      55
Field, algebraically closed      306
Field, computable      78 179
Field, perfect      311
Finite extension (field)      293
Finitely generated extension ring      52
Finitely generated ideal      26
Finitely generated K-algebra      434
Finitely generated R-module      135
First isomorphism theorem      34
Function      5
G-polynomial      457
Gaussian lemma      93
GCD (greatest common divisor)      4 38 43
Generating system      121 135
Grading      466
Greatest common divisor      4 38 43
Groebner      213
Groebner basis      207
Groebner basis, reduced      208
GROEBNERNEW1      225
GROEBNERNEW2      231
GROEBNERTEST      213
Group      16
Group, Abelien      16
Head coefficient      71 194
Head monomial      194
Head term      194
Height      323
Highest form      476
Hilbert basis theorem      86 145
Hilbert function      442
Hilbert nullstellensatz      312
Hilbert polynomial      448
Homogeneous      468
Homogeneous ideal      475
Homogeneous linear equation      244
Homogeneous system of linear equations      489
Homogenization      478
Homogenizing variable      478
Homomorphic image      24
Homomorphism of K-algebras      434
Homomorphism of K-vector spaces      120
Homomorphism of monoids      62
Homomorphism of R-modules      135
Homomorphism of rings      23
Homomorphism theorem      32 136
Homomorphism, canonical      31
Ideal      25
Ideal basis      26
Ideal membership test      86 215
Ideal power      336
Ideal product      335
Ideal quotient      265
Ideal, associated prime      352
Ideal, finitely generated      26
Ideal, homogeneous      475
Ideal, irreducible      358
Ideal, maximal      47
Ideal, monadic      358
Ideal, primary      351
Ideal, prime      47
Ideal, principal      26
Ideal, proper      25
Ideal, radical      147
Ideal, reducible      358
Ideal, trivial      25
Ideal, vanishing      263
Ideal, zero-dimensional      271
IDEALDIV1      266
IDEALDIV2      267
Idempotent      283
Identity      7
Inclusion map      7
Independent set      270
Independent set, algebraically      302
Independent set, algebraically maximal      303
Independent set, linearly      121
Independent set, linearly maximal      123
Independent set, maximally      270
Independent set, strongly      443
Independent set, strongly maximal      448
Indeterminate      69
Induction principle      1
Inhomogeneous system of linear equations      489
Injective      6
Inside-outside multiplication      25
Integral domain      20
Intersection      259
Inverse      16
Inverse block order      390
Inverse lexicographical order on $\mathbb{N}^n$      168
Inverse lexicographical term order      190
Inverse relation      150
Invertible (polynomial map)      330
Invertible (ring element)      20
Irreducible ideal      358
Irreducible polynomial      88
Irreducible ring element      87
Irreflexive relation      150
isolate      409
Isolated primary component      363
Isolating interval      408
Isolating intervals, set of      408
Isomorphic      24
Isomorphism of K-vector spaces      121
Isomorphism of monoids      63
Isomorphism of rings      23
Isomorphism theorem first      34
Isomorphism theorem second      36
ISOREC      411
ISOREFINE      412
Jacobinn conjecture      330
k-algebra      433
K-algebra, finitely generated      434
K-embedding      296
K-isomorphism      296
K-subalgebra      434
K-variety      327
K-vector space      119
K-vector space, computable      126
K-vector space, finite-dimensional      130
K-vector space, infinite-dimensional      131
Kernel      24 135
Koenig property      65
Kronecker factorization algorithm      11
lcm (least common multiple)      4 211
Least common multiple      44 211
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