Basic Algebra II: Second EditionCourier Corporation, 8 juin 2012 - 704 pages A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for more than three decades. Nathan Jacobson's books possess a conceptual and theoretical orientation; in addition to their value as classroom texts, they serve as valuable references. Volume II comprises all of the subjects usually covered in a first-year graduate course in algebra. Topics include categories, universal algebra, modules, basic structure theory of rings, classical representation theory of finite groups, elements of homological algebra with applications, commutative ideal theory, and formally real fields. In addition to the immediate introduction and constant use of categories and functors, it revisits many topics from Volume I with greater depth and sophistication. Exercises appear throughout the text, along with insightful, carefully explained proofs. |
Expressions et termes fréquents
a₁ abelian group absolute value algebraic over F algebraically closed artinian assume automorphism b₁ base bijective called central simple algebra clear closure coefficients commutative ring completely reducible congruence contains Dedekind domain define definition denote diag direct sum division algebra division ring elements endomorphisms equivalent exact sequence exercise exists extension field field F field of fractions finite group fractional ideal functor G₁ Galois group G Hence homomorphism implies injective integral invertible irreducible representations isomorphism left ideal lemma Let F Let G linear transformations M₁ matrix maximal ideal minimum polynomial mod-R monic monomorphism Moreover morphism multiplication N-algebra nilpotent noetherian non-zero obtain P₁ prime ideal Proof Proposition prove R-mod R-module R₁ representation of G result right module Show splitting field subalgebra subfield subgroup submodule subring subset suppose surjective theorem theory topology unique valuation ring vector space α α