{"product_id":"9789814603676","title":"LECTURE NOTES ON LOCAL RINGS","description":"The content in Chapter 1–3 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 Cohen–Macaulay rings and depth. In Chapters 4–6 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 7–9 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.\u003cstrong\u003eContents:\u003c\/strong\u003e  \u003cul\u003e   \u003cli\u003eDimension of a Local Ring\u003c\/li\u003e   \u003cli\u003eModules over a Local Ring\u003c\/li\u003e   \u003cli\u003eDivisor Theory\u003c\/li\u003e   \u003cli\u003eCompletion\u003c\/li\u003e   \u003cli\u003eInjective Modules\u003c\/li\u003e   \u003cli\u003eLocal Cohomology\u003c\/li\u003e   \u003cli\u003eDualizing Complexes\u003c\/li\u003e   \u003cli\u003eLocal Duality\u003c\/li\u003e   \u003cli\u003eAmplitude and Dimension\u003c\/li\u003e   \u003cli\u003eIntersection Multiplicities\u003c\/li\u003e   \u003cli\u003eComplexes of Free Modules\u003c\/li\u003e  \u003c\/ul\u003e  \u003cbr\u003e  \u003cstrong\u003eReadership:\u003c\/strong\u003e Graduate students and academic researchers with an interest in algebra, commutative algebra, algebra geometry, homological algebra and algebraic number theory.  \u003cb\u003eKey Features:\u003c\/b\u003e  \u003cul\u003e \u003cli\u003eAlthough the proofs are fairly short, the key points give readers the opportunity to supply details for their own satisfaction\u003c\/li\u003e \u003cli\u003eThe classical result of Auslander-Buchsbaum on unique factorization in a regular local ring is treated in a context of divisor and Picard groups, and this enlightens and connects to methods from number theory\u003c\/li\u003e \u003cli\u003eThis book contains original research of the late Professor Iversen that are not published in this form before\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47185355342064,"sku":"9789814603676","price":19.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814603676_p0.jpg?v=1763691457","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814603676","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}