Huishi Li — An Introduction to Commutative Algebra: From the Viewpoint of Normalization :: Электронная библиотека попечительского совета мехмата МГУ

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Huishi Li — An Introduction to Commutative Algebra: From the Viewpoint of Normalization

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Название: An Introduction to Commutative Algebra: From the Viewpoint of Normalization

Автор: Huishi Li

Аннотация:

Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure. It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry. Many worked examples and a number of problem (with hints) can be found in the volume. It is also a convenient reference for researchers who use basic commutative algebra.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 200

Добавлена в каталог: 19.06.2008

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Предметный указатель

Affine space      127
Algebra      79
Algebra homomorphism      79
Algebraic closure      28
Algebraic curve      160
Algebraic element      22
Algebraic field extension      22
Algebraic integer      102
Algebraic set      128
Algebraically closed      25
Algebraically independent      86
Ascending chain condition      6
Associate      9
Associated prime      95
Basis      40 48
Bilinear form      37
Characteristic      3
Closed set      144
Closure of a subset      145
Continuous function      145
Contraction of an ideal      71
Coordinate ring      136
Cuspidal curve      128
Cyclotomic field      109
Dedekind domain      125
Degree of a curve      151
Degree of a field extension      22
Degree of a polynomial      4
Dense subset      145
Direct sum of modules      48
Discrete valuation      60
Discrete valuation ring      61
Discriminant      104
Divisible      9
Divisor      9
Domain      3
DVR      61
Extension field      18
Extension of an ideal      71
Field      3
Field extension      18
Field of fractions      4
Field of rational functions      148
Finitely generated extension ring      80
Finitely generated ideal      2
Finitely generated module      47
Finitely generated subring      2
Fractional ideal      119
Free Abelian group      40
Free module      48
Group of units      9
Hypersurface      128
Ideal of an algebraic set      129
Induced topology      145
Inseparable field extension      24
Inseparable polynomial      22
Integral basis      102
Integral closure      83
Integral element      80
Integral extension      80
Integrally closed      83
Irreducible      9
Irreducible algebraic set      135
Irreducible component      142
Jacobson radical      57
Local ring      58
Local ring at P      149
Localization at P      72
Maximal condition      6
Maximal ideal      53
Maximal spectrum      53
Minimal polynomial      23

Module      45
Module homomorphism      47
Module of fractions      75
Module-finite      80
Monic polynomial      5
Multiplicative set      53
Multiplicity at P      155
Neighborhood of a point      144
Nilradical      56
Nodal curve      128
Noetherian module      49
Noetherian ring      6
Noetherian space      141
Nonsingular curve      153
Nonsingular point      153 160
Norm      35
Normal domain      90
Normalization      90
Normalization of a curve      161
Number field      102
Open set      144
p-adic valuation      62
PID      7
Plane curve      128
Pole set      147
Polynomial function      146
Polynomial mapping      138
Polynomial parametrization      139
Prime      11
Prime ideal      53
Prime spectrum      53
Prime subfield      3
Primitive element      25
Primitive polynomial      14
Principal ideal ring      7
Product topology      145
Proper factorization      9
Quadratic number field      108
Quotient module      47
R-basis      48
Radical ideal      132
Rational curve      163
Rational mapping      139
Rational parametrization      139
Reducible      9
Ring extension      79
Ring of algebraic integers      102
Ring of fractions      68
Separable field extension      24
Separable polynomial      22
Simple extension field      18
Simple point      153
Singular point      153
Splitting field      19
Square-free      80
Subalgebra      79
Submodule      46
Symmetric polynomial      29
Tangent line      153
Topological space      144
topology      144
Total polynomial      34
Trace      35
Transcendental element      22
Transcendental field extension      22
Trivial divisor      9
Twisted cubic      128
UFD      11
Unimodular      41
UNIT      3
Valuation ring      65
Z-basis      40
Zariski topology      134

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