Modern Abstract Algebra 1

Cover & Errata from MathSciNet review Title Preface Symbols and Notations Contents of Volume One Contents of Volume Two I. Monoids and Semi-groups §1.1. Composition §1.2. Monoid §1.3. Mappings and homomorphisms §1.4. Free monoid and monoid generated by a set §1.5. Construction of a free monoid §1.6. Semi-group Problems with hints or solutions for Chapter I II. Groups §2.1. Definition of a group §2.2. Abelian groups (i.e. commutative groups) §2.3. Subgroups §2.4. Cosets and conjugate elements §2.5. Group homomorphisms §2.6. Normal subgroups, simplicity and semi-simplicity §2.7. Quotient Groups (i.e. factor groups) §2.8. Free group and group generated by a set §2.9. Construction of a free group §2.10. Derived chain and lower central series §2.11. Solvable groups and nilpotent groups §2.12. Series and chains formed by some subgroups of a group §2.13. Some theorems concerning normal subgroups §2.14. Exact sequence and group extension §2.15. Direct product and semi-direct product §2.16. General classification of group extensions §2.17. Action of a set on a group §2.18. Preliminary notions on cohomology theory of groups §2.19. Factor-sets of a group extension §2.20. Cohomological consideration of extensions of non-abelian groups Problems with hints or solutions for Chapter II III. On Rings §3.1. Rings §3.2. Boolean rings, integral domains, division rings and fields §3.3. Ideals §3.4. Prime ideals, and ideals generated by subsets §3.5. Maximal and minimal ideals §3.6. Ring-homomorphisms §3.7. Quotient rings (i.e. "factor rings") §3.8. Direct Sum §3.9. Chain conditions, Artin and Noether rings §3.10. Filtration and graded structure §3.11. Ore condition and ring of fractions §3.12. Nilpotency §3.13. Radicals, quasi-regularity, and semi-simplicity §3.14. Group rings §3.15. Euclidean rings Problems with hints or solutions for Chapter III v. 1. Monoids, groups, and rings. v. 2. Modules, linear endomorphisms, and algebras.