ABSTRACT ALGEBRA

By O. KIZIU

CONTENTS STARRED SECTIONS AND CHAPTERS MAY BE SKIPPED AT ?RST READING 1 SEMIGROUPS 3 SUBGROUPS 4 HOMOMORPHISMS 5 THE ISOMORPHISM THEOREMS 6 FREE GROUPS II STRUCTURE OF GROUPS 1 DIRECT PRODUCTS *2 THE KRULL-SCHMIDT THEOREM 4 SYMMETRIC GROUPS 6 SMALL GROUPS 7 COMPOSITION SERIES *8 THE GENERAL LINEAR GROUP 9 SOLVABLE GROUPS *10 NILPOTENT GROUPS III RINGS 2 SUBRINGS AND IDEALS 3 HOMOMORPHISMS 6 POLYNOMIALS IN SEVERAL VARIABLES *7 FORMAL POWER SERIES 8 PRINCIPAL IDEAL DOMAINS *9 RATIONAL FRACTIONS 7 PRESENTATIONS I GROUPS 10 UNIQUE FACTORIZATION DOMAINS 11 NOETHERIAN RINGS IV FIELD EXTENSIONS 2 EXTENSIONS 8 TRANSCENDENTAL EXTENSIONS 9 SEPARABILITY V GALOIS THEORY 1 SPLITTING FIELDS 5 POLYNOMIALS 6 CYCLOTOMY 7 NORM AND TRACE 8 SOLVABILITY BY RADICALS 9 GEOMETRIC CONSTRUCTIONS 2 REAL FIELDS 3 ABSOLUTE VALUES 5 EXTENSIONS 8 HENSEL’S LEMMA 9 FILTRATIONS AND COMPLETIONS VII COMMUTATIVE RINGS 1 PRIMARY DECOMPOSITION 2 RING EXTENSIONS 3 INTEGRAL EXTENSIONS 5 DEDEKIND DOMAINS 6 ALGEBRAIC INTEGERS 7 GALOIS GROUPS 8 MINIMAL PRIME IDEALS * * * 11 REGULAR MAPPINGS 1 DE?NITION 2 HOMOMORPHISMS 5 VECTOR SPACES 6 MODULES OVER PRINCIPAL IDEAL DOMAINS 8 CHAIN CONDITIONS IX SEMISIMPLE RINGS AND MODULES 1 SIMPLE RINGS AND MODULES 2 SEMISIMPLE MODULES 4 PRIMITIVE RINGS 5 THE JACOBSON RADICAL 7 REPRESENTATIONS OF GROUPS 8 CHARACTERS 1 EXACT SEQUENCES 4 INJECTIVE MODULES XI CONSTRUCTIONS 2 PROPERTIES OF HOM 3 DIRECT LIMITS 4 INVERSE LIMITS 6 PROPERTIES OF TENSOR PRODUCTS 7 DUAL MODULES 8 FLAT MODULES 1 COMPLEXES 2 RESOLUTIONS 3 DERIVED FUNCTORS 4 EXT 5 TOR * * * * * * * * * * * * * 6 UNIVERSAL COEF?CIENT THEOREMS 9 GLOBAL DIMENSION 1 ALGEBRAS OVER A RING 2 THE TENSOR ALGEBRA 3 THE SYMMETRIC ALGEBRA 5 TENSOR PRODUCTS OF ALGEBRAS 6 TENSOR PRODUCTS OF FIELDS 1 DE?NITIONS 5 BOOLEAN LATTICES XV UNIVERSAL ALGEBRA 2 WORD ALGEBRAS 3 VARIETIES 4 SUBDIRECT PRODUCTS 1 DE?NITION AND EXAMPLES 2 FUNCTORS 3 LIMITS AND COLIMITS 4 COMPLETENESS *5 ADDITIVE CATEGORIES 9 TRIPLEABILITY 10 VARIETIES