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The present book is an English translation of Algebre Locale - Multiplicites published by Springer-Verlag as no. 11 of the Lecture Notes series. The original text was based on a set of lectures, given at the College de France in 1957-1958, and written up by Pierre Gabriel.
Local algebra is the branch of commutative algebra that studies commutative local rings and their modules. In practice, a commutative local ring often arises as the result of the localization of a ring at a prime ideal. The concept of local rings was introduced by Wolfgang Krull in 1938 under the name Stellenringe.
En Álgebra abstracta, los anillos locales son ciertos anillos comparativamente simples y que sirven para describir el comportamiento local de las funciones definidas sobre variedades algebraicas o variedades diferenciables.
The goal of these notes is to provide an overview of some facts from local algebra, and more importantly, how they relate to algebraic geometry. The content is based on the course Math 233B. Theory of Schemes, taught by Dennis Gaitsgory in Spring 2010 at Harvard1.
1 de ene. de 2003 · Attached to any element a of an algebra A, there is an algebra A a called the local algebra of A at a. The inheritance between the properties of an algebra and those of its local algebra is...
Local rings are the bread and butter of algebraic geometry. Definition 10.18.1. A local ring is a ring with exactly one maximal ideal. If R is a local ring, then the maximal ideal is often denoted mR and the field R/mR is called the residue field of the local ring R.
In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/module R, so that it consists of fractions such that the denominator s belongs to a given subset S of R.
