Modern Abstract Algebra

Description

Cover & Errata from MathSciNet review Title Preface Symbols and Notations Contents of Volume Two Contents of Volume One IV. On Modules §4.1. Modules over a group or a ring §4.2. Submodules, quotient modules, faithful module and annihilator §4.3. Module homomorphisms §4.4. Sum and direct sum of modules §4.5. Chain condition, Artin and Noether modules, maximum and minimum conditions §4.6. Submodule generated by a subset and R-linear independence §4.7. Simplicity, semi-simplicity and composition series §4.8. Free modules §4.9. Tensor product §4.10. Exact sequences, extensions, projective and injective modules §4.11. Chain complexes, homology and cohomology modules Problems with hints or solution for Chapter IV V. On Module Homomorphisms §5.1. Dimensionality of a Gamma-module §5.2. Simplicity and semi-simplicity of a Gamma-endo §5.3. Projection mapping and ring of Gamma-endos §5.4. Fitting decomposition w.r.t. a Gamma-endo §5.5. Some properties of polynomials of a K-endo §5.6. Minimal polynomial of a K-endo §5.7. Eigen vectors and eigen values of a K-endo §5.8. Characteristic polynomial and eigen-space decomposition of a K-endo §5.9. Primary-component decomposition w.r.t. a K-endo §5.10. Bilinear forms and inner products on K-modules §5.11. Group representations Problems with hints or solutions for Chapter V VI. On Algebras §6.1. Algebras, ideals and quotient algebras §6.2. Derivation mappings §6.3. Algebra homomorphisms §6.4. Free algebras §6.5. Tensor algebras and symmetric algebras §6.6. Exterior product and exterior algebra §6.7. Lie algebras §6.8. Derivation mappings, solvability, nilpotency and semi-simplicity in Lie algebras §6.9. Extensions and representations Problems with hints or solution for Chapter VI Index of definitions