Lectures in Abstract Algebra: Theory of fields and Galois theoryVan Nostrand, 1951 - 323 pages The three volume Lectures are based on Jacobson's graduate lectures on algebra at Johns Hopkins and Yale in the 1940's and early 1950's, and are very careful, comprehensive and classical in style, giving a general treatment of abstract algebra. The first volume gives a comprehensive introduction to abstract algebra and its basic concepts. The second volume deals with the theory of vector spaces, accompanied by examples and exercises. The third and final volume addresses field theory and Galois theory, and is not an easy read for the casual student, but a serious student who works at the material will be repaid for their efforts. All volumes include a considerable number of exercises are given that vary greatly in difficulty, while the texts in general are example-driven and user-friendly. |
Table des matières
SECTION 1 Extension of homomorphisms | 1 |
Algebras | 7 |
Tensor products of vector spaces | 10 |
Droits d'auteur | |
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Expressions et termes fréquents
a₁ algebraic extension algebraically closed algebraically independent assume automorphism clear closure commutative consider contains cyclic defined elements equation equivalent exists extension field field of characteristic finite dimensional extension finite dimensional Galois formally real Galois group group G Hence Hom G homomorphism implies indeterminates integer irreducible isomorphism leading coefficient Lemma Let f(x linear linearly disjoint mapping maximal ideal minimum polynomial morphism multiplication nomial non-archimedean non-zero normal obtain order isomorphism ordered field ordered group p-independent p₁ polynomial f(x positive degree Proof prove purely inseparable rational numbers real closed field real numbers real valuation result roots of f(x satisfies separable algebraic sequence Show solvable splitting field subalgebra subfield subgroup subring suppose Theorem tion transcendency basis transcendental U₁ valuation ring vector space