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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.
Order of a minor90 Order of a power series35—43604 Order of a square submatrix90 Order relative to a quasilocal ring85153 Order relative to an ideal94607 Order-type56 Ordered (additive abelian) monoid209 Ordered abelian group41604 Ordered completion55 Ordered disjoint union683 Ordered domain53 Ordered field53 Ordered set33603 Orderwise complete55 Orderwise completion55 Ordinal3451—5256 Orthogonal group62 Orthogonal idempotents343 Orthogonal to343 Overfield, overring, etc.6600—601 Overgroup4 Overnormal domain80606 Overposet381 overset4598 parabola63 Paraboloid63 PARAMETER65 Parameter ideal300619 Parameters for a local ring300619 Parametrically65 Parametrize150 Parenthetical colon118 Parenthetical Colon Lemma385624 Parity526600 Parshall98 Partial order33 Partially ordered set33603 Partition53771599 Pdim Lemma (Supplemental)389 Perfect field515630 Perfect Field Theorem (Basic)519 Perfect group680 Permutation523600 Permutation isomorphism660 Permutation matrix513629679 Perpendicular64 PID13602 PID Lemma479 PID Theorem479 PID Unimodularity Lemma486 PIDs (modules over)479—481 PIR348—354621 Plane curve606371102149 Plane curves with their tangents counted in terms of tangential multiplicities557 Plane curves with their total transforms consisting of proper transforms and powers of the exceptional line557 Pluecker98 Po33 Point-set is zero dimensional149 Points at finite distance68550 Points at infinity67—68550 polar63—70 Pole63 Polynomial9—12168602647 Polynomial automorphism92—9498 Polynomial extension of a homomorphism425444 Polynomial in 34 Polynomial module444 Polynomial ring9—12602 Polynomial ring in a (not necessarily finite) family of indeterminates168647 Polynomial rings (ideals or maximal ideals in and regularity of the localization of)423—431 Polynomials in a Family (Not NECESSARILY FINITE) of Indeterminates168647 Portion at finite distance (or affine portion)68550 POSET33603 Positive portion of a graded module400626 Positive portion of a graded ring212 Positive upper segment372 Possible Real Ranks686 Power of a homomorphism445 Power series34—39604 Power series ring34—39604 Power set3344604 Predecessor (immediate)375623681 Prefree resolution312 Premodel156633 Preprojective resolution312434628 Primary decomposition104107114 Primary decomposition summary134—137 Primary decomposition uniqueness118—119 Primary Ideal Blowup Theorem553 Primary ideal colons109—110 Primary ideal for a prime conditions109 Primary ideal or submodule109608 Primary ideals intersections109—110224 Primary nonirreducible ideal114 Primary not power of prime110 Primary submodule colons112—113 Primary submodule conditions (for modules over any ring)113170—171195—197 Primary submodule intersections113 Prime Avoidance Corollary339 Prime avoidance lemma339621 Prime ideal717601 Prime ideal (nonmaximal coprincipal)376 Prime Ideal Blowup Theorem560 Prime ideal conditions218 Prime ideal generalities128—129 Prime ideals avoidance128—129339 Prime ideals intersect in rad zero128 Prime power group655 Prime power not primary110 Prime power orbit657 Prime power subgroup655 Prime power subgroup (existence of)659 Primitive (permutation) group665 Primitive element150514629 Primitive Element Theorem150 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 Lemma665 Princeton Book200 Principal component121 Principal ideal7601 Principal ideal domain13602 Principal ideal rings348—354621 Principal ideal theorem231579 Principal Ideal Theorem with its Corollary232 Principal isolated subgroup376681 Principal rank686 Principle of idealization of Nagata225—229613 Processes on roots75 Product spaces (diagonals and intersections in)431—433 Product Theorem (Codimension)418627 Products of ideals or modules108 Projection101 Projective decomposition of ideals and varieties545—547 Projective dimension (pdim) of a module312—313620 Projective dimension (prodim) of a subintegrally graded ring535 Projective dimension of a variety535542 Projective Dimension Theorem543 Projective general linear group62 Projective Inclusion Relations Theorem544 Projective model157—159633 Projective module312442620 Projective modules over polynomial rings (or over PIDs)441—514628 Projective normalization529630 Projective Normalization Theorem532630 Projective nullstellensatz544 Projective Primitive Element Theorem544
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