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Название: Algebra
Автор: Hungerford T.W.
Аннотация:
Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents. The guiding philosophical principle throughout the text is that the material should be presented in the maximum usable generality consistent with good pedagogy. Therefore it is essentially self-contained, stresses clarity rather than brevity and contains an unusually large number of illustrative exercises. The book covers major areas of modern algebra, which is a necessity for most mathematics students in sufficient breadth and depth.
243 174199ff -invariant subspace356 (Greatest) lower bound14 A.C.C.see "Ascending chain condition" Abel's theorem308 Abelian extension field292 Abelian field extension292 Abelian group2470ff76ff Abelian group defined by generators and relations343ff Action of group on set88ff Additive notation for groups25293870 Adjoining a root236 Adjoint Associativity214 Adjoint functor477ff Adjoint pair of functors477ff Affine variety409 Aitin, E.vi251252288 Algebra module(s)451 Algebra(s)226ff450ff Algebra(s) ideal228 Algebraic algebra453 Algebraic closure259ff Algebraic dependence311ff Algebraic element233453 Algebraic extension field233ff Algebraic field extension233ff Algebraic independence311ff Algebraic number242 Algebraic set409 Algebraically (in)dependent311ff Algebraically closed field258 Algorithm multilinear function349 Alternating group49 Annihilator206388417 Anti-isomorphism330 Antisymmetric relation13 Artinian module372ff Artinian rings372ff419ff421435ff Ascending central series100 Ascending chain condition83372ff Associate135 Associated prime ideal380387 Associative binary operation24 Automorphism30119 Automorphism of a group3090 Axiom of Choice13 Axiom of class formation2 Axiom of extensionality2 Axiom of pair formation6 Baer lower radical444ff Basis71181 Bijective function5 Bilinear function(s)211349 Bilinear map211349 Bimodule202 Binary operation24 Binomial coefficient118 Binomial theorem118 Boolean ring120 Cancellation24116 Canonical bilinear map211 Canonical epimorphism43125172 Canonical forms337 Canonical injection60130173 Canonical injections60130173 Canonical middle linear map209 Canonical projection859130173 Cardan's formulas310 cardinal number16ff Cardinal number(s) inequalities17 Cardinality16 Cartesian product67ff Category52ff464ff Category, concrete55 Cauchy's theorem93 Cayley — Hamilton theorem367369 Cayley's theorem90 Center of a group3491 Center of a ring122 Central idempotents135 Central simple division algebra456 centralizer89 Chain13 Chain conditions83ff372ff Chain conditions on submodule(s)372ff Char R119 Characteristic of a ring119 Characteristic polynomial366ff Characteristic polynomial of a linear transformation366ff Characteristic polynomial of an endomorphism(s)366ff Characteristic polynomials of matrices366ff Characteristic space368 Characteristic subgroups103 Characteristic values367 Characteristic vectors367 Chinese remainder theorem131 Choice function15 class2ff Class equation9091 Classical adjoint353 Classical adjoint matrix353 Classification of finite groups96ff Closed intermediate field247 Closed object410 Closed subgroups247 Closed under a binary operation31 Codomain3 Coefficients of Polynomial(s)150 Coequalizer482 Cofactor352 Cohen, I.S.388 Coimage176 Cokernel176 Cokernel of a morphism483 Column rank336339 Column space336 Column vector333 Commutative binary operation24 Commutative diagram4 Commutative group24 Commutative ring115 Commutator102 Commutator subgroup102 Companion matrices358 Companion matrix358 Comparable elements13 Complement3 Complete direct sum59 Complete lattice15 Complete ring of quotients144 Complete set of coset representatives39 Completely reducible module437 Composite function4 Composite functor468 Composite morphism52 Composite subfield233 Composition series108375 Concrete category55 Congruence modulo a subgroup37 Congruence modulo m12 Congruence relation27 Conjugacy class89 Conjugate elements or subgroups89 Conjugation88 Constant polynomial150 Constant term150154 Constructible number239 Content of a polynomial162 Continuum Hypothesis17
Contraction of an ideal146398 Contravariant functor466 Contravariant horn functor466 Conway, C.T.xiii Coordinate ring413 Coproduct54ff Coset38ff Couniversal object57 Covariant functor465 Covariant horn functor465 Cramer's rule354 Cycles46 Cyclic extension field289ff292 Cyclic field extension289ff Cyclic group3235ff Cyclic module171 Cyclic subgroup(s)32 Cyclic submodule(s)171 Cyclic subspace356 Cyclotomic extension297ff Cyclotomic extension field297ff Cyclotomic polynomial166298 D.C.C.see "Descending chain condition" Decomposition of a linear transformation355ff Dedekind domain401ff Degree of a field element234 Degree of a monomial157 Degree of a polynomial157158 Degree of inseparability285ff DeMorgan's laws3 Dense ring418 Dense ring of endomorphism(s)418 Density theorem420 Denumerable set16 Derivative161 Derived subgroup102 Descending chain condition83372ff Determinant351ff Determinant of an endomorphism354 Determinants of matrices351ff Diagonal matrix328 Difference cokernel482 Difference kernel482 Dihedral group50 DIMENSION185ff Direct factor63 Direct product2659ff130131173 Direct product of group(s)2659ff Direct product of module(s)173 Direct product of ring(s)130131 Direct sum6062ff173175 Direct sum of group(s)6062 Direct sum of matrices360 Direct sum of module(s)173175 Direct summand63437 Discrete valuation ring404 Discriminant270 Discriminant of Polynomial(s)270 Disjoint cycles47 Disjoint permutations47 Disjoint sets3 Disjoint union58 Divisible abelian group195ff Divisible group195ff Division algebras227456ff Division algorithm11158 Division ring116 Division ring of real quaternions117461 Domain of a function3 Double dual205 Dual basis204 Dual category466 Dual map204 Dual module203ff Dual statement54 Eigenspace368 Eigenvalues367ff Eigenvalues of a linear transformation367 Eigenvalues of matrices368 Eigenvectors367ff Eigenvectors of a linear transformation367 Eigenvectors of matrices368 Eisenstein's criterion164 Elementary column operation338 Elementary divisors80225357361 Elementary divisors of a linear transformation357 Elementary divisors of matrices361 Elementary Jordan matrices359 Elementary Jordan matrix359 Elementary matrices338 Elementary row operation338 Elementary row or column operation338 Elementary symmetric functions252 Elementary transformation matrix338 Embedded prime384 Embedded prime ideal384 Embedding119 Empty set3 Empty word64 End A116 Endomorphism(s) of a group30 Endomorphism(s) ring116179415 Epic morphism480 Epimorphism30118170 Epimorphism in a category480 Equality2 Equalizer482 Equipollent sets15 Equivalence class6 Equivalence in a category53 Equivalence relation6 Equivalent matrices332335ff Equivalent series109375 Euclidean algorithm141 Euclidean Domain139 Euclidean ring139 Euler function297 Evaluation homomorphism153 Even permutation48 Exact sequence175ff Exact sequence of module(s)175ff Expansion of a determinant along a row353 Exponentiation in a group28 Exponentiation of cardinal numbers22 Extendible automorphism251260 Extension field231ff Extension of an ideal145 Extension ring394ff External direct product130 External direct sum60173 External weak direct product60 Factor group42ff Factorization in commutative rings135ff Factorization in polynomial rings157ff Factors of a series107375 Faithful module418 Field116230ff Field extension231ff Field of rational functions233 Finite dimensional algebra227 Finite dimensional field extension231 Finite dimensional vector space186 Finite division ring462 Finite field278ff462 Finite group2492ff96ff Finite set16 Finitely generated abelian group76ff Finitely generated abelian groups76ff343ff Finitely generated extension field231232 Finitely generated group32
-invariant subspace 
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