Algebra: Chapter 0American Mathematical Soc., 2009 - 713 sidor Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references. |
Innehåll
| 1 | |
Chapter II Groups first encounter | 41 |
Chapter III Rings and modules | 119 |
Chapter IV Groups second encounter | 187 |
Chapter V Irreducibility and factorization in integral domains | 243 |
Chapter VI Linear algebra | 305 |
Chapter VII Fields | 385 |
Chapter VIII Linear algebra reprise | 483 |
Chapter IX Homological algebra | 559 |
| 699 | |
Back Cover | 715 |
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abelian category abelian group additive functor algebraically closed assume Autk F automorphisms bijection cohomology cokernel commutative ring composition construction contains coproducts Corollary corresponding cyclic defined Definition degree denoted diagram direct sum divisor element epimorphism example Exercise exists fact factors field extension follows free modules function Galois extension group G group homomorphism group of order hence Hint HomR identity induced injective integral domain inverse irreducible polynomials isomorphism kernel Lemma Let F Let G matrix maximal ideal monomorphism morphism multiplication Noetherian nontrivial nonzero normal subgroup notation notion objects obtained operation precisely prime ideals prime integer projective resolution Proof Proposition Prove quasi-isomorphism quotient R-Mod R-module reader resp ring homomorphism roots splitting field statement subgroup of G submodule subset surjective tensor Theorem trivial unique universal property vector space verify Z/nZ