A COURSE IN ALGEBRA VOLUME 1

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Ouvrage 9789810240615 : A COURSE IN ALGEBRA VOLUME 1
A COURSE IN ALGEBRA
by Y Fan, Q Y Xiong & Y L Zheng (Wuhan University, P R China)
This volume is based on the lectures given by the authors at Wuhan University and Hubei University in courses on abstract algebra. It presents the fundamental concepts and basic properties of groups, rings, modules and fields, including the interplay between them and other mathematical branches and applied aspects.
Contents:
ùPreliminaries: Sets ùLogic ùRelations ùMaps ùZorn's Lemma ùGroups: Transformations and Permutations ùGroups ùSubgroups ùHomomorphisms, Isomorphisms ùCosets ùNormal Subgroups, Quotient Groups ùHomomorphism Theorems ùCyclic Groups, Orders of Elements ùDirect Products ùRings: Fundamentals ùZero Divisors, Invertible Elements ùIdeals, Residue Rings ùHomomorphism Theorems ùPrime Ideals, Maximal Ideals ùDirect Sums ùFraction Fields of Integral Domains ùPolynomial Rings ùFactorial Rings ùPolynomial Rings over Factorial Rings ùModules: Modules ùHomomorphisms ùDirect Products, Direct Sums ùExact Sequences of Homomorphisms ùFree Modules, Matrices over Rings ùMatrices over Division Rings ùMatrices over Commutative Rings ùAlgebras over Commutative Rings ùTensor Products ùProjective Modules, Injective Modules ùFields: Subfields and Extensions ùSingle Extensions ùAlgebraic Extensions ùSplitting Fields, Normal Extensions ùTwo Applications ùSeparability, Multiple Roots ùFinite Fields ùCoding ùp-adic Numbers ùQuaternions
Readership: First- and second-year students in algebra.

Auteur : FAN
Editeur : WORLD SCIENTIFIC
Nombre de pages : 280
Date de publication : 07 2000

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