ALGEBRAS, RINGS AND MODULES

By A. PANIL

GROUPS AND SUBGROUPS DE?NITIONS AND EXAMPLES QUOTIENT GROUPS, HOMOMORPHISMS AND NORMAL SUBGROUPS SYLOW THEOREMS SOLVABLE AND NILPOTENT GROUPS GROUP RINGS AND GROUP REPRESENTATIONS MASCHKE THEOREM PROPERTIES OF IRREDUCIBLE REPRESENTATIONS CHARACTERS OF GROUPS ORTHOGONALITY RELATIONS AND THEIR APPLICATIONS MODULAR GROUP REPRESENTATIONS NOTES AND REFERENCES CHAPTER 2 QUIVERS AND THEIR REPRESENTATIONS TENSOR ALGEBRA OF A BIMODULE APPENDIX TO SECTION 2 5 MORE ABOUT DYNKIN AND EXTENDED DYNKIN (= EYCLIDEAN) DIAGRAMS CHAPTER 3 REPRESENTATIONS OF POSETS AND OF ?NITE DIMENSIONAL ALGEBRAS REPRESENTATIONS OF POSETS CHAPTER 4 FROBENIUS ALGEBRAS AND QUASI-FROBENIUS RINGS MONOMIAL IDEALS AND NAKAYAMA PERMUTATIONS OF SEMIPERFECT RINGS QUASI-FROBENIUS RINGS THE SOCLE OF A MODULE AND A RING OSOFSKY THEOREM FOR PERFECT RINGS SOCLES OF PERFECT RINGS DUALITY IN NOETHERIAN RINGS SEMIPERFECT RINGS WITH DUALITY FOR SIMPLE MODULES SELF-INJECTIVE RINGS QUIVERS OF QUASI-FROBENIUS RINGS REJECTION LEMMA CHAPTER 5 RIGHT SERIAL RINGS HOMOLOGICAL DIMENSIONS OF RIGHT NOETHERIAN RINGS STRUCTURE OF RIGHT ARTINIAN RIGHT SERIAL RINGS RIGHT HEREDITARY RIGHT SERIAL RINGS SEMIPRIME RIGHT SERIAL RINGS CARTAN MATRIX FOR A RIGHT ARTINIAN RIGHT SERIAL RING TILED ORDERS OVER DISCRETE VALUATION RINGS AND EXPONENT MATRICES DUALITY IN TILED ORDERS TILED ORDERS AND FROBENIUS RINGS Q-EQUIVALENT PARTIALLY ORDERED SETS INDICES OF TILED ORDERS FINITE MARKOV CHAINS AND REDUCED EXPONENT MATRICES FINITE PARTIALLY ORDERED SETS, (0,1)-ORDERS AND ?NITE MARKOV CHAINS TILED ORDERS AND WEAKLY PRIME RINGS GLOBAL DIMENSION OF TILED ORDERS CYCLIC GORENSTEIN MATRICES CAYLEY TABLES OF ELEMENTARY ABELIAN 2-GROUPS QUASI-FROBENIUS RINGS AND GORENSTEIN TILED ORDERS SUGGESTIONS FOR FURTHER READING