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Northcott D.G. — Ideal theory
Northcott D.G. — Ideal theory

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Название: Ideal theory

Автор: Northcott D.G.


Ideal theory is important not only for the intrinsic interest and purity of its logical structure but because it is a necessary tool in many branches of mathematics. In this introduction to the modern theory of ideals, Professor Northcott assumes a sound background of mathematical theory but no previous knowledge of modern algebra. After a discussion of elementary ring theory, he deals with the properties of Noetherian rings and the algebraic and analytical theories of local rings. In order to give some idea of deeper applications of this theory the author has woven into the connected algebraic theory those results which play outstanding roles in the geometric applications.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 118

Добавлена в каталог: 17.11.2013

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Предметный указатель
Analytic independence      67
Ascending chain condition      19
Basis theorem of Hilbert      26
Calculus of ideals      4
Cauchy sequence      85
Completion of a local ring      92
Composition series      51
Concordant rings      87
Contraction of an ideal      38 44
Convergence in a local ring      84
Dimension of a local ring      63
Dimension of an ideal      57
Divisor      78
Divisor of zero      25
Embedded prime ideal      17
Extension of an ideal      38 45
Extension ring      38
Field      25
Finitely generated ideal      9
Full ring of quotients      40
Generalized ring of quotients      44
Homomorphism      32
Ideal      4
Ideal, generated by a set      8
Indeterminates      25
Integral closure      73
Integral dependence      73
Integral divisor      79
Integral domain      25
Irreducible ideal      21
Irredundant decomposition      15
Isolated component of an ideal      17
Isolated set of prime ideals      18
Isomorphism      32
Kernel of a homomorphism      34
Length of a primary ideal      52
Local ring      48
Maximal condition for ideals      20
Maximal ideal      37
Maximal prime ideal      23
Minimal ideal bases      69
Minimal prime ideals of an ideal      13
Multiplicatively closed set      17
Natural homomorphism      34
Nilpotent element      36
Noetherian ring      19
Normal decomposition      15
Nucleus of a homomorphism      34
Null divisor      79
Ordinary ring of quotients      44
Polynomial ring      25
Power series      89
Primary ideal      10
Primary ring      54
Prime ideal      9
Prime ideal, belonging to an ideal      17
Principal ideal      9
Proper ideal      4
Radical of an ideal      13
Rank of an ideal      57
Regular local ring      70
Residue class      33
Residue class ring      34
Residue field of a local ring      63
Ring      1 4
Ring of quotients      41 44
S-component      17
Symbolic prime power      51
System of parameters      64
Union of a family of sets      13
UNIT      24
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