Abhyankar S.S. — Lectures on Algebra Volume 1 :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Abhyankar S.S. — Lectures on Algebra Volume 1

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Lectures on Algebra Volume 1

Автор: Abhyankar S.S.

Аннотация:

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel, "Lectures on Algebra II", will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 746

Добавлена в каталог: 28.03.2010

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

Предметный указатель

Minimal free resolution      312
Minimal generating set      49 605
Minimal homogenization      536
Minimal modelic affine space      152
Minimal normal subgroup      665
Minimal polynomial      21 580 603
Minimal prefree resolution      312
Minimal primes      218 231 265
Minimal Primes Theorem      265 584 616
Minimal prospectral variety      534
Minimal spectral variety      115 148 609
Minimal spectrum      231 265 609
Minimum (or smallest or least) element in a poset      381
Minor      90 607
Modelic affine space      152
Modelic blowup      159—161 237 611 631
Modelic blowup (dominating)      566 631
Modelic Blowup Theorem      159
Modelic Blowup Theorem (its Supplementary portion)      567 595
Modelic proj      157—159 237 631—632
Modelic proj of a semihomogeneous domain      536 631
Modelic Proj Theorem      157
Modelic projective space      157—159 540—541 547—548
Modelic spec      152 611 631
Models      105 154—161 631—634
Modified discriminant      26 515 516 603 629
Module      8 108 602
Module generation for local rings      236
Module theoretic power      204 612
Module theoretic restricted power      204 612
Modules over PIDs      479—481
Modules over univariate polynomial rings      444—479
Modulized Hilbert degree      397 626
Modulized Hilbert function      393 626
Modulized Hilbert polynomial      393 626
Modulized Hilbert subdegree      393 626
Modulized Hilbert transcendence      393 626
Monic (polynomial)      10 17 78 162 606
Monoid      6 602
Monoidal Theorem (First to Twelfth)      571—577
Monoidal transform      570—571 632
Monoidal transform along a valuation      570—571 632
Monoidal transform centered at      570
Monoidal transformation      558 569
Monomial ideals      168—170
Monomorphism      7—9 599—601
Monomorphism splits      445
Moore      4 61
Multiple Ring Extension Lemma      269 616
Multiple roots and separable polynomials      407 603
Multiplicative      3 6 600
Multiplicative (also called algebra-theoretic) direct sum      340—341 621
Multiplicative set      118—119 609
Multiplicity      65
Multiply the roots      76
Multitransitive group      662 678
Multivariable      30
Multivariate      104
Multivariate ideal extensions      235
Nagata      597
Nagata's principle of idealization      225—229 613
Nakayama lemma      219—220 613
Narrative discourse and logical formality      201
Natural epimorphism for homogeneous local ring to homogeneous function field      542—543
Natural epimorphism for local ring to function field      147—149
Natural injection      203—205 612
Natural isomorphism for function fields      147—149
Natural isomorphism for homogeneous function fields      542—543
Natural map      12
Natural projection      203—205 612
Naturally graded ring      209
Near-field      6
Negative of a loset      373 683
Neighborhoods of a point (first, second, etc.)      161
Newton      16
Newton's Symmetric Function Theorem      16 639
Newton's Theorem      43 76 604
Nilpotent      109
Nilpotent set      217
Nilpotents modulo an ideal      217
Nilradical      261—262 616
Nilradical Theorem      262
Nodal and cuspidal cubics      160
Node      71
Noether (Emmy)      104 247 597
Noether (Max)      98 161
Noether Normalization Theorem      248 615
Noether Normalization Theorem and homogeneous normalization      401—408 626
Noetherian conditions      113 218—219
Noetherian model      156 633
Noetherian module      113 129—132 608
Noetherian ring      86 104—107 129—132 607
Noetherian: ACC $\Leftrightarrow$ MXC $\Leftrightarrow$ NNC      113
Nonarchimedean valuations      164
Noncancellative quasiordered monoids      596
Nonconstant polynomial      10—11
Nonempty lower segment      374
Nongoing down for nondomains      582
Nongoing down for nonnormal domains      581
Nongoing down for nonzerodivisors      582
Nonmaximal coprincipal prime ideal      376
Nonnegative portion      365
Nonnegatively graded ring      209
NonP (= opposite property)      109 120
Nonsingular      69
Nonsingular model      156—159 633
Nonzero principal isolated subgroup      376
Nonzerodivisor      109 120
Nonzerodivisor (multiplicative) set      120
Norm      642
Norm (behavior under finite algebraic field extension)      643
Norm (properties of)      645
Normal (field) extension      635
Normal (to)      64
Normal crossing      70 567—569 634
Normal Crossing Lemma      569
Normal crossings, equimultiple locus and resolved ideals      567—569
Normal domain or ring      78 242 606
Normal Local Ring Lemma      358 622
Normal model      156 633
Normal ring or domain      78 242 606
Normal series      124
Normal subgroup      4 599
Normality Lemma      667
Normalization      529 633
Normalization basis      248 615
Normalization Theorem and Limitations on it      248 591 615
Normalize      654
normalizer      654
Normalizer of prime power subgroup      656
Null ring      6 600
Nullstellensatz (including its Spectral and Projective versions)      151 260 265 544 616
Obvious Lemma      662
Odd permutation      5 25 600
One dimensional CM local rings      308
One Dimensional GST Ring Characterization Theorem      307 620
One dimensional special GST rings      310
Operational dehomogenization map      549
Operational homogenization or minimal homogenization map      551
Orbit      652
Orbit Counting Lemma      653
Orbit set (= orbset)      653
Orbit-Stabilizer Lemma      652
Ord Valuation Lemma      280 618
Ord Valuation Lemma, Another aspect      299 618
Ord Valuation Theorem      153
Order isomorphism      55
Order Lemma      657
Order of a group      4 599
Order of a meromorphic series      35—43 604

Order of a minor      90
Order of a power series      35—43 604
Order of a square submatrix      90
Order relative to a quasilocal ring      85 153
Order relative to an ideal      94 607
Order-type      56
Ordered (additive abelian) monoid      209
Ordered abelian group      41 604
Ordered completion      55
Ordered disjoint union      683
Ordered domain      53
Ordered field      53
Ordered set      33 603
Orderwise complete      55
Orderwise completion      55
Ordinal      34 51—52 56
Orthogonal group      62
Orthogonal idempotents      343
Orthogonal to      343
Overfield, overring, etc.      6 600—601
Overgroup      4
Overnormal domain      80 606
Overposet      381
overset      4 598
parabola      63
Paraboloid      63
PARAMETER      65
Parameter ideal      300 619
Parameters for a local ring      300 619
Parametrically      65
Parametrize      150
Parenthetical colon      118
Parenthetical Colon Lemma      385 624
Parity      5 26 600
Parshall      98
Partial order      33
Partially ordered set      33 603
Partition      5 37 71 599
Pdim Lemma (Supplemental)      389
Perfect field      515 630
Perfect Field Theorem (Basic)      519
Perfect group      680
Permutation      5 23 600
Permutation isomorphism      660
Permutation matrix      513 629 679
Perpendicular      64
PID      13 602
PID Lemma      479
PID Theorem      479
PID Unimodularity Lemma      486
PIDs (modules over)      479—481
PIR      348—354 621
Plane curve      60 63 71 102 149
Plane curves with their tangents counted in terms of tangential multiplicities      557
Plane curves with their total transforms consisting of proper transforms and powers of the exceptional line      557
Pluecker      98
Po      33
Point-set is zero dimensional      149
Points at finite distance      68 550
Points at infinity      67—68 550
polar      63—70
Pole      63
Polynomial      9—12 168 602 647
Polynomial automorphism      92—94 98
Polynomial extension of a homomorphism      425 444
Polynomial in $\omega$       34
Polynomial module      444
Polynomial ring      9—12 602
Polynomial ring in a (not necessarily finite) family of indeterminates      168 647
Polynomial rings (ideals or maximal ideals in and regularity of the localization of)      423—431
Polynomials in a Family (Not NECESSARILY FINITE) of Indeterminates      168 647
Portion at finite distance (or affine portion)      68 550
POSET      33 603
Positive portion of a graded module      400 626
Positive portion of a graded ring      212
Positive upper segment      372
Possible Real Ranks      686
Power of a homomorphism      445
Power series      34—39 604
Power series ring      34—39 604
Power set      33 44 604
Predecessor (immediate)      375 623 681
Prefree resolution      312
Premodel      156 633
Preprojective resolution      312 434 628
Primary decomposition      104 107 114
Primary decomposition summary      134—137
Primary decomposition uniqueness      118—119
Primary Ideal Blowup Theorem      553
Primary ideal colons      109—110
Primary ideal for a prime conditions      109
Primary ideal or submodule      109 608
Primary ideals intersections      109—110 224
Primary nonirreducible ideal      114
Primary not power of prime      110
Primary submodule colons      112—113
Primary submodule conditions (for modules over any ring)      113 170—171 195—197
Primary submodule intersections      113
Prime Avoidance Corollary      339
Prime avoidance lemma      339 621
Prime ideal      7 17 601
Prime ideal (nonmaximal coprincipal)      376
Prime Ideal Blowup Theorem      560
Prime ideal conditions      218
Prime ideal generalities      128—129
Prime ideals avoidance      128—129 339
Prime ideals intersect in rad zero      128
Prime power group      655
Prime power not primary      110
Prime power orbit      657
Prime power subgroup      655
Prime power subgroup (existence of)      659
Primitive (permutation) group      665
Primitive element      150 514 629
Primitive Element Theorem      150
Primitive Element Theorem (Basic version)      520
Primitive Element Theorem (Projective version)      544
Primitive Element Theorem (Supplemented version)      529
Primitive root of one (or unity)      517
Primitive Root of Unity (or One)      517
Primitivity Lemma      665
Princeton Book      200
Principal component      121
Principal ideal      7 601
Principal ideal domain      13 602
Principal ideal rings      348—354 621
Principal ideal theorem      231 579
Principal Ideal Theorem with its Corollary      232
Principal isolated subgroup      376 681
Principal rank      686
Principle of idealization of Nagata      225—229 613
Processes on roots      75
Product spaces (diagonals and intersections in)      431—433
Product Theorem (Codimension)      418 627
Products of ideals or modules      108
Projection      101
Projective decomposition of ideals and varieties      545—547
Projective dimension (pdim) of a module      312—313 620
Projective dimension (prodim) of a subintegrally graded ring      535
Projective dimension of a variety      535 542
Projective Dimension Theorem      543
Projective general linear group      62
Projective Inclusion Relations Theorem      544
Projective model      157—159 633
Projective module      312 442 620
Projective modules over polynomial rings (or over PIDs)      441—514 628
Projective normalization      529 630
Projective Normalization Theorem      532 630
Projective nullstellensatz      544
Projective Primitive Element Theorem      544

1 2 3 4 5 6

О проекте