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Abhyankar S.S. — Lectures on Algebra Volume 1

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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

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Предметный указатель

Subscript notation      659
Subset      4 598
Subset injection      384
Subset injection (it is the obvious injective map of a subset into the set)      384
Substitution homomorphism      38
Substitution map      12 38
Substitution map for polynomial tuples      485
Subvariety      104
Subvariety (also with qualification of proper or reducible or irreducible)      147 148 535 542
Sum of homomorphisms      445
Sums of ideals or modules      108
Supplemental Pdim Lemma      389
Supplementary (additional) Modelic Blowup Theorem      567 595
Supplementary (First and Second) Dimension Theorem      266—267
Supplemented Primitive Element Theorem      529
Support and annihilator of a module      197
Support and quasiprimary decomposition of a submodule      198
Support of a function or map in general (denoted by supp)      168 203 376 612
Support of a meromorphic series or power series or polynomial (or of a function or map leading to these, denoted by Supp)      34—43 604
Support of a module (denoted by supp)      197 333—334
Support of an element in a direct sum (denoted by supp)      209
Supremum      381
Surds      27
surface      30—31 60 63—65 104 149—150
Surjection      3 598
Surjective      3 584 598
Suslin      442
Suslin's Localization      688
Suslin's Localization Lemma      502
Suslin's Theorem      442 497 500
Sylow subgroup      657
Sylow transitivity      657
Sylow's theorem      658
Sylvester      98 100 166 176 433 628
Symmetric function      638
Symmetric function (elementary)      637—640
Symmetric group      3 25 600
Symmetric rational function      639
Symmetric relation      37
Symplectic group      62
System of imprimitivity      664
Syzygies      433 628
Syzygies (homogeneous)      435
Syzygy      434 628
Syzygy Theorem (Hilbert)      441
Tacnode      71
Tangent      63—71
Tangential multiplicity      577
Tight assassinator = colorful (somewhat like the word annihilator) long form of tass      117 168—170 216 609
Tight associator      117 168—170 216 609
Topologically equivalent      399
Torsion subgroup      54
Total quotient ring      137—138
Total quotient rings of reduced noetherian rings and their normalizations      340—348
Total transform      160—161 557—559
Trace      642
Trace (behavior under finite algebraic field extension)      643
Trace (properties of)      645
Transcendence basis      12 49 602
Transcendence degree      12 149 250 602 615
Transcendental element      12 602
transform      160—161 557—559 767—568 632
Transforms of one or two ideals relative to local ring triples      567—568 632
Transitive action      656 678
Transitive group      656 678
Transitive relation      37
Translation of coordinates      70
transportation      660
TRANSPOSE      90 607
Transposition      5 25 600
Transvection matrix      481 679
Transvection Theorem      482
Transversally      567
Triple point      65
Trivariate      31
Trivial block      664
Trivial valuation      41 355 622
Triviality of associated graded ring      587
Tschirnhausen      59
Tuple notation and functional notation      204
Two-transitive action (of special linear and projective specual linear group) on projective space      678
Type of a graded ring is an additive abelian monoid      206
UFD = unique factorization domain      5 13 19 81—83 602
UFD Lemma      386
UFD Theorem      391 624

ujjain      596
Underlying additive abelian group      9
Underlying homomorphism (of an algebra)      340 621
Unequicharacteristic = nonequicharacteristic (quasilocal ring)      555
Uniformization (thesis)      171
Unimodular column      484
Unimodular row      484
Unimodular tuple      484
union      4 598
Unique factorization domain      5 13 19
Unique factorization in polynomial rings      81
Unique factorization in power series rings      82 393
Unique factorization in regular local rings      385—392 624
Unit ideal      7 601
Unit Ideals in Polynomial Rings      47 672
Unitary group      62
Units in a matrix ring      62
Units in a power series ring      39
Units in a ring      13 602
Univariate      14
Univariate ideal extensions      235 616
Univariate ideal extensions lemma together with its sharper versions called Simple and Multiple Ring Extension Lemmas      235 268—269 616
Univariate polynomial and power series rings (heights of ideals)      300
Universally catenarian      268 616
University Algebra      597
Unmixed (ideal)      281 354 618
Unmixedness theorem holds      281 618
Unresolved (ideal in a ring)      568 634
Unsolvability Theorem      16
Upper bound in a poset      33
Upper segment (positive)      372
Valuation      39—43 188—192 604
Valuation Characterization Theorem      156
Valuation Existence Theorem      155
Valuation extension theorem      155
Valuation function      274 617 681
Valuation functions (Theorem about them)      275 617 681
Valuation Maximality Theorem      155
Valuation ring      41 155 604
Valuation ring of a field      154 382 623
Valuation ring of a field over a ring      154
Valuation theoretic composition      687
Valuation, trivial or real or real discrete      355 622—623
Valuations and L'Hospital's Rule      201
Value group      41 604
Vandermonde Determinant Theorem      514 515
Variable      13 36
Varieties in affine or spectral space      146—153
Varieties in modelic space      154—160
Varieties in projective space      534—552
Variety      31 104—108 146—160 534—552
Veblen      98
Vector      9 602
Vector space      9 602
Vector space basis      49
Weak Zorn property      44
Wedderburn      7
Weierstrass      84
Weierstrass degree      84 606
Weierstrass division theorem      84—89 606
Weierstrass preparation theorem      83—89 98 606
Well ordered power      377 682
Well ordered product      377 682
Well ordered set      33 603
Well ordering      32—33 44—52 603—604
Weyl      63
Wo      33
Word problem      1
Woset      33 603
Young      98
Zariski      98 597
Zariski ring      219—220 613
Zariski rings characterization      228
Zariski — Samuel's book (cited in Limitations on Normalization Theorem)      591—592
Zassenhaus      7
Zero Dimensional GST (Gorenstein) Ring Characterization Lemma      303
Zero ideal      7 601
Zero matrix      182
Zerodivisor      109 120 217
Zerodivisor set      120 217 609
Zerodivisor Theorem      217 612
Zerodivisors modulo a submodule      217
Zerodivisors modulo an ideal      217
Zorn property      33 44
Zorn's lemma      32—33 44—52 604—605

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