Algebra I: chapters 1-3
This is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'AlgA]bre'. It gives a thorough exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects: groups, actions, rings, fields. The second chapter studies the properties of modules and linear maps, especially with respect to the tensor product and duality constructions. The third chapter investigates algebras, in particular tensor algebras. Determinants, norms, traces and derivations are also studied.
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Description of formal mathematics 2 Theory of sets 3 Ordered sets
The AXmodule associated with an AmoduIe endo
Groups and groups with operators
98 other sections not shown
A-algebra A-linear A-module structure algebra associative basis bijective called canonical homomorphism canonical injection canonical mapping commutative group commutative ring compatible composition series containing decomposition Deduce defined Definition denoted direct sum direct system endomorphism equivalence relation exact sequence Exercise exists finite group formula graded group G group with operators hence Hom(E homogeneous identified identity element implies indexing set induction integer inverse isomorphism kernel law of composition left A-module left ideal left resp Lemma Let G linear mapping magma matrix Mo(X module monoid morphism multiplication necessary and sufficient nilpotent non-empty non-zero normal stable subgroup normal subgroup notation ordered pair permutation prime number quotient group respect ring homomorphism Set Theory Show stable subgroup stable subset subgroup of G submodule subring subspace Suppose surjective Sylow subgroup tensor product Theorem two-sided ideal unique vector space whence