Unit Groups of Classical Rings

Part 1 Introduction: notation and terminology; assumed results. Part 2 Algebraic units: finiteness of the class group; the Dirichlet-Chevalley- Hasse Unit Theorem; existence of real and conjugate independent units; units in quadratic fields and pure cubic fields. Part 3 The unit group of the integers []: relations between the unit groups; Dirichlet L-series and class number formulas; cyclotomic units; bass independence theorem. Part 4 Multiplicative groups of fields: multiplicative structure of some classical fields; multiplicative groups of local fields;intermediate fields; Kneser's theorem and related results; fields with free multiplicative groups modulo torsion; embedding groups; multiplicative groups under field extensions. Part 5 Multiplicative groups of division rings: commutativity conditions; subnormal subgroups - preliminary results and main theorems; periodic multiplicative commutators; periodic subnormal subgroups; free subgroups. Part 6 Rings with cyclic unit groups: finite commutative rings with a cyclic group of units: rings with a cyclic group of units - the general case. Part 7 Finite generation of unit groups: general results; finitely generated extensions; the Whitehead group and stability theorem; finite generation of GL n(R). Part 8 Unit groups of group rings: definitions and elementary properties; trace of idempotents; units of finite order; trivial units; conjugacy of group bases; torsion-free complements; units in commutative group rings. (Part contents)