Rings and Things and a Fine Array of Twentieth Century Associative Algebra

Part I. An array of twentieth century associative algebra: Direct product and sums of rings and modules and the structure of fields Introduction to ring theory: Schur's lemma and semisimple rings, prime and primitive rings, nil, prime and Jacobson radicals Direct sum decompositions of projective and injective modules Direct product decompositions of von Neumann regular rings and self-injective rings Direct sums of cyclic modules When injectives are flat: Coherent FP-injective rings Direct decompositions and dual generalizations of Noetherian rings Completely decomposable modules and the Krull-Schmidt-Azumaya theorem Polynomial rings over Vamosian and Kerr rings, valuation rings and Prufer rings Isomorphic polynomial rings and matrix rings Group rings and Maschke's theorem revisited Maximal quotient rings Morita duality and dual rings Krull and global dimensions Polynomial identities and PI-rings Unions of primes, prime avoidance, associated prime ideals, ACC on irreducible ideals and annihilator ideals in commutative rings Dedekind's theorem on the independence of automorphisms revisited Part II. Snapshots of some mathematical friends and places: Snapshots of some mathematical friends and places Index to part II (snapshots) Bibliography Register of names Index of terms and authors of theorems.