Description

Book Synopsis
Presents an account of noncommutative Noetherian rings. This book covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory.

Table of Contents
Preliminaries Basic theory: Some Noetherian rings Quotient rings and Goldie's theorem Structure of semiprime Goldie rings Semiprime ideals in Noetherian rings Some Dedekind-like rings Dimensions: Krull dimension Global dimension Gelfand-Kirillov dimension Extensions: The Nullstellensatz Prime ideals in extension rings Stability $K_0$ and extension rings Examples: Polynomial identity rings Enveloping algebras of Lie algebras Rings of differential operators on algebraic varieties References Index of notation Index.

Noncommutative Noetherian Rings

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    A Hardback by American Mathem American Mathem

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      View other formats and editions of Noncommutative Noetherian Rings by American Mathem American Mathem

      Publisher: MP-AMM American Mathematical
      Publication Date: 2/28/2001 12:00:00 AM
      ISBN13: 9780821821695, 978-0821821695
      ISBN10: 0821821695

      Description

      Book Synopsis
      Presents an account of noncommutative Noetherian rings. This book covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory.

      Table of Contents
      Preliminaries Basic theory: Some Noetherian rings Quotient rings and Goldie's theorem Structure of semiprime Goldie rings Semiprime ideals in Noetherian rings Some Dedekind-like rings Dimensions: Krull dimension Global dimension Gelfand-Kirillov dimension Extensions: The Nullstellensatz Prime ideals in extension rings Stability $K_0$ and extension rings Examples: Polynomial identity rings Enveloping algebras of Lie algebras Rings of differential operators on algebraic varieties References Index of notation Index.

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