Lecture Notes On Local Rings

The content in Chapter 13 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machinery is also supported by CohenMacaulay rings and depth. In Chapters 46 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 79 are not so standard and introduce the reader to the generalizations of modules to complexes of modules. Some of Professor Iversen's results are given in Chapter 9. Chapter 10 is about Serre's intersection conjecture. The graded case is fully exposed. The last chapter introduces the reader to Fitting ideals and McRae invariants. Contents: Dimension of a Local RingModules over a Local RingDivisor TheoryCompletionInjective ModulesLocal CohomologyDualizing ComplexesLocal DualityAmplitude and DimensionIntersection MultiplicitiesComplexes of Free ModulesReadership: Graduate students and academic researchers with an interest in algebra, commutative algebra, algebra geometry, homological algebra and algebraic number theory.