Divisor Theory in Module Categories
Published on 3. June 2016
130 pages
978-1-4832-5720-4 (ISBN)
Description
North-Holland Mathematics Studies, 14: Divisor Theory in Module Categories focuses on the principles, operations, and approaches involved in divisor theory in module categories, including rings, divisors, modules, and complexes. The book first takes a look at local algebra and homology of local rings. Discussions focus on Gorenstein rings, Euler characteristics of modules, Macaulay rings, Koszul complexes, Noetherian and coherent rings, flatness, and Fitting's invariants. The text then explains divisorial ideals, including divisors, modules of dimension one, and higher divisorial ideals. The manuscript ponders on spherical modules and divisors and I-divisors. Topics include construction, Euler characteristics of Inj (A), change of rings and dimensions, spherical modules, resolutions and divisors, and elementary properties. The text is a valuable source of information for mathematicians and researchers interested in divisor theory in module categories.
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Content
PrefaceChapter 1 : Local Algebra 1.1 . Noetherian and Coherent Rings 1.2 . Local Rings 1.3 . Flatness 1.4 . Fitting's InvariantsChapter 2 : Homology of Local Rings 2.1 . Koszul Complexes 2.2 . Depth 2.3 . Macaulay Rings 2.4 . Projective and Injective Dimensions 2.5 . Euler Characteristics of Modules 2.6 . Gorenstein Rings 2.7 . Rings of Type OneChapter 3 : Divisorial Ideals 3.1 . Composition in Id(A) 3.2 . Divisors 3.3 . Modules of Dimension One Appendix . Higher Divisorial IdealsChapter 4 : Spherical Modules and Divisors 4.1 . A Theorem of Gruson 4.2 . Change of Rings and Dimensions 4.3 . Spherical Modules 4.4 . Elementary Properties 4.5 . Resolutions and DivisorsChapter 5 : I-Divisors 5.1 . Construction 5.2 . Euler Characteristics of Inj(A) 5.3 .Divisors on Inj(A)oBibliographyIndex
