Northcott D. G. — An introduction to homological algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Northcott D. G. — An introduction to homological algebra

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Название: An introduction to homological algebra

Автор: Northcott D. G.

Аннотация:

Homological algebra, because of its fundamental nature, is relevant to many branches of pure mathematics, including number theory, geometry, group theory and ring theory. Professor Northcott's aim is to introduce homological ideas and methods and to show some of the results which can be achieved.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 1960

Количество страниц: 282

Добавлена в каталог: 31.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

0-sequence      13
Abbreviated notation      12
Abstract mappings      30
Acyclic complex over a module      76
Additive category      32
Additive functor      35
Ascending chain condition      144
Associative law for tensor products      160
Augmentation homomorphism of a complex over a module      76
Augmentation ideal of a monoid-ring      217
Augmentation mapping of a monoid-ring      216
Augmentation translation      75
Bihomomorphism      156
Bimodule      155
Boundaries      224
Boundary homomorphism      59
Category      31
Chains      223
Coboundaries      224
Cochains      224
Cocycles      224
Cohomology theory of monoids      221
Coimage of a mapping      6
Cokernel of a mapping      6
Commutative diagram      5
Commutator subgroup      230
Complete derived sequence of a group      252
Complete free resolution of Z      259
Complete representation as a direct product      10
Complete representation as a direct sum      10
COMPLEX      59
Complex associated with a module      75
Connected sequence of functors      114
Connecting homomorphism      56
Contravariant functor      33
Covariant functor      33
Cycles      223
Cyclic module      138
Diagram      46
Differentiation homomorphism      59
Direct epimorphism      12
Direct factor      12
Direct monomorphism      12
Direct product of modules      9
Direct sum of modules      9
Direct summand      12
Divisible module      269
Domain of a mapping      32
Epimorphism      4
Equivalence mapping      32
Equivalence of functors      36
Exact functor      38
Exact homology sequence      61
Exact sequence      14
Extension functors      129
Extension module      3
External direct sum      9
Factor module      3
Free group generated by a set      213
Free module      7
Free module generated by a set      8
Free monoid generated by a set      212
Free resolution      77
Functor of modules      36
Functor of one variable      33
Functor of several variables      34
Generators of a module      7
Global dimension of a ring      138
Group-ring      216
Homological codimension      204
Homological dimension of a module      134
Homology functor      52
Homology modules of a complex      60
Homology theory of a monoid      219
Homomorphism of a connected sequence of functors      115
Homomorphism of modules      3
Homomorphism of monoids      212
Homotopic translations      62
Ideal-theoretic dimension      202

Identity mapping      4
image of a mapping      6
Induced mapping      5
Inductive system      271
Injective complex      75
Injective module      67
Injective representation as a direct sum      10
Injective resolution of a module      76
Injective resolution of an exact sequence      81
Integral domain      176
Internal direct sum      11
Irreducible word      212
Isomorphism of a connected sequence of functors      115
Isomorphism of modules      4
Kernel of a mapping      6
Left complex      60
Left complex over a module      76
Left exact functor      40
Left-derived functors      110
Linear functor      35
Local ring      185
Maximal ideal      181
Minimal injective extension      270
Module of fractions      167
Module with respect to a monoid      214
Module with respect to a ring      1
Module with trivial operators      214
Monoid      211
Monoid ring      216
Monomorphism      4
Multiplicatively closed set      167
Natural mapping      3
Natural transformation of functors      35
Noether's Equations      276
Noetherian module      144
Noetherian ring      146
Norm homomorphism      250
Norm of a homomorphism      252
Normal sequence      196
Null homotopic translation      62
Partially ordered set      270
Prime ideal      186
Principal ideal      176
Principal ideal domain      176
Projective complex      75
Projective dimension of a module      134
Projective module      63
Projective representation as a direct product      10
Projective resolution of a module      76
Projective resolution of an exact sequence      80
Proper ideal      181
range of a mapping      32
Regular local ring      203
Residue module      3
Right complex      60
Right complex over a module      75
Right derived functors      102
Right exact functor      40
Ring of fractions      168
Semi simple ring      144
Similar diagrams      46
Simple module      142
Simply ordered set      270
Special modules with respect to a finite group      253
Split exact sequence      14
Standard homogeneous resolution of Z      225
Standard non homogeneous resolution of Z      227
Submodule      3
Tensor product of mappings      19
Tensor product of modules      16
Torsion functors      122
Totally ordered set      270
Translation category of diagrams      47
Translation of diagrams      47
Translation over a homomorphism      78
Weak global dimension      150
Weak homological dimension of a module      149
Well ordered set      270
Zero-divisor for a module      196
Zorn's lemma      271

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