ALGEBRAS, RINGS AND MODULES
1 1 BASIC CONCEPTS AND EXAMPLES 1 2 MODULES AND HOMOMORPHISMS 1 3 CLASSICAL ISOMORPHISM THEOREMS 1 4 DIRECT SUMS AND PRODUCTS 1 6 NOTES AND REFERENCES CHAPTER 2 DECOMPOSITIONS OF RINGS 2 3 LATTICES BOOLEAN ALGEBRAS AND RINGS 2 4 FINITELY DECOMPOSABLE RINGS 2 5 NOTES AND REFERENCES CHAPTER 3 ARTINIAN AND NOETHERIAN RINGS 3 1 ARTINIAN AND NOETHERIAN MODULES AND RINGS 3 2 THE JORDAN-H¨OLDER THEOREM 3 3 THE HILBERT BASIS THEOREM 3 5 THE RADICAL OF ARTINIAN RINGS 3 6 A CRITERION FOR A RING TO BE ARTINIAN OR NOETHERIAN 3 7 SEMIPRIMARY RINGS 3 8 NOTES AND REFERENCES 4 3 THE HOM FUNCTORS 4 4 BIMODULES 4 5 TENSOR PRODUCTS OF MODULES 4 7 DIRECT AND INVERSE LIMITS 4 8 NOTES AND REFERENCES CHAPTER 5 PROJECTIVES, INJECTIVES AND ?ATS 5 1 PROJECTIVE MODULES 5 2 INJECTIVE MODULES 5 3 ESSENTIAL EXTENSIONS AND INJECTIVE HULLS 5 4 FLAT MODULES 5 5 RIGHT HEREDITARY AND RIGHT SEMIHEREDITARY RINGS 5 6 HERSTEIN-SMALL RINGS 5 7 NOTES AND REFERENCES CHAPTER 6 HOMOLOGICAL DIMENSIONS 6 1 COMPLEXES AND HOMOLOGY FREE RESOLUTIONS 6 2 PROJECTIVE AND INJECTIVE RESOLUTIONS DERIVED FUNCTORS 6 3 THE FUNCTOR TOR 6 4 THE FUNCTOR EXT 6 5 PROJECTIVE AND INJECTIVE DIMENSIONS 6 6 GLOBAL DIMENSIONS 6 7 NOTES AND REFERENCES CHAPTER 7 INTEGRAL DOMAINS 7 1 PRINCIPAL IDEAL DOMAINS 7 2 FACTORIAL RINGS 7 5 POLYNOMIAL RINGS OVER FACTORIAL RINGS 7 6 THE CHINESE REMAINDER THEOREM 7 7 SMITH NORMAL FORM OVER A PID 7 8 FINITELY GENERATED MODULES OVER A PID 7 9 THE FROBENIUS THEOREM 7 10 NOTES AND REFERENCES 8 1 INTEGRAL CLOSURE 8 2 DEDEKIND DOMAINS 8 3 HEREDITARY DOMAINS 8 4 DISCRETE VALUATION RINGS 8 5 FINITELY GENERATED MODULES OVER DEDEKIND DOMAINS 8 7 NOTES AND REFERENCES 9 1 ORE CONDITION CLASSICAL RINGS OF FRACTIONS 9 4 NOTES AND REFERENCES CHAPTER 10 SEMIPERFECT RINGS 10 1 LOCAL AND SEMILOCAL RINGS 10 3 LIFTING IDEMPOTENTS SEMIPERFECT RINGS 10 4 PROJECTIVE COVERS THE KRULL-SCHMIDT THEOREM 10 6 EQUIVALENT CATEGORIES 10 7 THE MORITA THEOREM 10 8 NOTES AND REFERENCES CHAPTER 11 QUIVERS OF RINGS 11 3 QUIVERS (?NITE DIRECTED GRAPHS) 11 4 THE PRIME QUIVER OF A SEMIPERFECT RING 11 5 THE PIERCE QUIVER OF A SEMIPERFECT RING 11 7 THE PRIME QUIVER OF AN FDD-RING 11 8 THE QUIVER ASSOCIATED WITH AN IDEAL 11 9 THE LINK GRAPH OF A SEMIPERFECT RING CHAPTER 12 SERIAL RINGS AND MODULES 12 2 SEMIPERFECT PRINCIPAL IDEAL RINGS 12 3 SERIAL TWO-SIDED NOETHERIAN RINGS 12 4 PROPERTIES OF SERIAL TWO-SIDED NOETHERIAN RINGS 12 5 NOTES AND REFERENCES 13 1 FINITELY PRESENTED MODULES 13 2 THE DROZD-WAR?ELD THEOREM ORE CONDITION FOR SERIAL RINGS 13 3 MINORS OF SERIAL RIGHT NOETHERIAN RINGS 13 6 NOTES AND REFERENCES CHAPTER 14 SEMIPERFECT SEMIDISTRIBUTIVE RINGS 14 3 QUIVERS OF SPSD-RINGS 14 4 SEMIPRIME SEMIPERFECT RINGS 14 5 RIGHT NOETHERIAN SEMIPRIME SPSD-RINGS 14 6 QUIVERS OF TILED ORDERS 14 7 QUIVERS OF EXPONENT MATRICES 14 9 NOTES AND REFERENCES